Existence and uniqueness of positive solutions to nonlinear fractional differential equation with integral boundary conditions

In this paper, we consider the following nonlinear fractional three-point boundary-value problem:

A bound for the error of the Ritz method in the case of the Lidstone problem for a singular differential equation of fourth order

For the Lidstone boundary-value problem

Solvability of boundary-value problems for nonlinear fractional differential equations

We consider the existence of nontrivial solutions of the boundary-value problems for nonlinear fractional differential equations

Periodic Positive Solution to a Class of Singular Second-Order Ordinary Differential Equations

This paper studies the existence of a positive solution to the second-order periodic boundary value problem

Solution of Initial Value Problems with Monogenic Initial Functions in Banach Spaces with L p -Norm

This paper deals with the initial value problem of the type

Asymptotically autonomous parabolic evolution equations

We study the long-term behaviour of the parabolic evolution equation $\[u'(t)=A(t)u(t)+f(t), t>s,\quad u(s)=x. \]$\[u'(t)=A(t)u(t)+f(t), t>s,\quad u(s)=x. \] If A(t) A(t) converges to a sectorial operator A with s(A)?i \Bbb R = ? \sigma(A)\cap i \Bbb R =\emptyset as t?￥ t\to\infty , then the evolution family solving the homogeneous problem has exponential dichotomy. If also f(t)? f_￥ f(t)\to f_\infty , then the solution u converges to the 'stationary solution at infinity', i.e., lim_t?￥u(t) = -A\sp-1f_￥=:u_￥,        lim_t?￥u￠(t)=0,        lim_t?￥A(t)u(t)=Au_￥. \lim_{t\to\infty}u(t)= -A\sp{-1}f_\infty=:u_\infty, \qquad \lim_{t\to\infty}u'(t)=0, \qquad \lim_{t\to\infty}A(t)u(t)=Au_\infty. .     

Optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations

Nonimprovable, in a sense sufficient conditions guaranteeing the unique solvability of the problem

Some Oscillation Theorems for Second Order Differential Equations

In this paper we establish some oscillation or nonoscillation criteria for the second order half-linear differential equation

Global asymptotic stability for half-linear differential systems with generalized almost periodic coefficients

The following system considered in this paper:

On the problem of determining the parameter of a parabolic equation

We study the boundary-value problem of determining the parameter p of a parabolic equation

Viability for nonlinear multi-valued reaction–diffusion systems

In this paper we consider a nonlinear evolution reaction–diffusion system governed by multi-valued perturbations of m-dissipative operators, generators of nonlinear semigroups of contractions. Let X and Y be real Banach spaces, ${\mathcal{K}}In this paper we consider a nonlinear evolution reaction–diffusion system governed by multi-valued perturbations of m-dissipative operators, generators of nonlinear semigroups of contractions. Let X and Y be real Banach spaces, K{\mathcal{K}} be a nonempty and locally closed subset in \mathbbR ×X×Y, A:D(A) í X\rightsquigarrow X, B:D(B) í Y\rightsquigarrow Y{\mathbb{R} \times X\times Y,\, A:D(A)\subseteq X\rightsquigarrow X, B:D(B)\subseteq Y\rightsquigarrow Y} two m-dissipative operators, F:K ? X{F:\mathcal{K} \rightarrow X} a continuous function and G:K \rightsquigarrow Y{G:\mathcal{K} \rightsquigarrow Y} a nonempty, convex and closed valued, strongly-weakly upper semi-continuous (u.s.c.) multi-function. We prove a necessary and a sufficient condition in order that for each (t,x,h) ? K{(\tau,\xi,\eta)\in \mathcal{K}}, the next system

{ lc u￠(t) ? Au(t)+F(t,u(t),v(t))    t 3 tv￠(t) ? Bv(t)+G(t,u(t),v(t))    t 3 tu(t)=x,    v(t)=h, \left\{ \begin{array}{lc} u'(t)\in Au(t)+F(t,u(t),v(t))\quad t\geq\tau \\ v'(t)\in Bv(t)+G(t,u(t),v(t))\quad t\geq\tau \\ u(\tau)=\xi,\quad v(\tau)=\eta, \end{array} \right.      12. Non-autonomous stochastic evolution equations and applications to stochastic partial differential equations      Mark C. Veraar 《Journal of Evolution Equations》2010,10(1):85-127 In this paper we study the following non-autonomous stochastic evolution equation on a Banach space E: $({\rm SE})\quad \left\{\begin{array}{ll} {\rm d}U(t) = (A(t)U(t) +F(t,U(t)))\,{\rm d}t + B(t,U(t))\,{\rm d}W_H(t), \quad t\in [0,T], \\ U(0) = u_0.\end{array}\right.$ Here, ${(A(t))_{t\in [0,T]}}In this paper we study the following non-autonomous stochastic evolution equation on a Banach space E: (SE)    {ll dU(t) = (A(t)U(t) +F(t,U(t))) dt + B(t,U(t)) dWH(t),     t ? [0,T], U(0) = u0.({\rm SE})\quad \left\{\begin{array}{ll} {\rm d}U(t) = (A(t)U(t) +F(t,U(t)))\,{\rm d}t + B(t,U(t))\,{\rm d}W_H(t), \quad t\in [0,T], \\ U(0) = u_0.\end{array}\right.      13. Precise Asymptotic Formulas for Semilinear Eigenvalue Problems      T. Shibata 《Annales Henri Poincare》2001,2(4):713-732 . We consider the nonlinear Sturm-Liouville problem¶¶-u"(t) = | u(t) | p-1u(t) - lu(t), t ? I :=(0,1), u(0) = u(1) = 0 -u'(t) = \mid u(t)\mid^{p-1}u(t) - \lambda u(t), t \in I :=(0,1), u(0) = u(1) = 0 ,¶¶ where p > 1 and l ? R \lambda \in {\bf R} is an eigenvalue parameter. To investigate the global L2-bifurcation phenomena, we establish asymptotic formulas for the n-th bifurcation branch l = ln (a) \lambda = \lambda_n (\alpha) with precise remainder term, where a \alpha is the L2 norm of the eigenfunction associated with l \lambda .      14. On the time continuity of entropy solutions      Cl��ment Canc��s  Thierry Gallou?t 《Journal of Evolution Equations》2011,11(1):43-55 We show that any entropy solution u of a convection diffusion equation ?t u + div F(u)-Df(u) = b{\partial_t u + {\rm div} F(u)-\Delta\phi(u) =b} in Ω × (0, T) belongs to C([0,T),L1loc(W)){C([0,T),L^1_{\rm loc}({\Omega}))} . The proof does not use the uniqueness of the solution.      15. The Shuddering Pendulum      Stuart S. Antman 《Journal of Nonlinear Science》2011,21(4):595-638 This paper treats the rich mathematical structure of the (dimensionless) equation of motion governing the behavior of an elastically restrained simple pendulum subject to a downward force of magnitude f(t) applied to its bob with $\dot{f}(t)>0$\dot{f}(t)>0 for all t>0 and f(t)→∞ as t→∞: [(q)\ddot]+2n[(q)\dot] +q = f(t)sinq.\ddot{\theta}+2\nu\dot{\theta} +\theta= f(t)\sin\theta.      16. Quenching phenomena for a non-local diffusion equation with a singular absorption      Raúl Ferreira 《Israel Journal of Mathematics》2011,184(1):387-402 In this paper we study the quenching problem for the non-local diffusion equation ut(x,t) = òW J(x - y)u(y,t)dy + ò\mathbbRN\W J(x - y)dy - u(x,t) - lu - p(x,t) {u_t}(x,t) = \int\limits_\Omega {J(x - y)u(y,t)dy + \int\limits_{{\mathbb{R}^N}\backslash \Omega } {J(x - y)dy - u(x,t) - \lambda {u^{ - p}}(x,t)} }      17. Renormalized solution for Stefan type problems: existence and uniqueness      Noureddine Igbida  Karima Sbihi  Petra Wittbold 《NoDEA : Nonlinear Differential Equations and Applications》2010,17(1):69-93 We consider a class of nonlinear degenerate problems of Stefan type: $u_t- \Delta w -\nabla F(u,w)= g(\cdot,u), \ w\in \beta(u)$ where β is a maximal monotone graph in ${\mathbb{R}^2,}We consider a class of nonlinear degenerate problems of Stefan type: ut- Dw -?F(u,w) = g(·,u),  w ? b(u)u_t- \Delta w -\nabla F(u,w)= g(\cdot,u), \ w\in \beta(u)      18. Long-time behavior of solutions to Hamilton–Jacobi equations with quadratic gradient term      Yasuhiro Fujita  Paola Loreti 《NoDEA : Nonlinear Differential Equations and Applications》2009,16(6):771-791 We study a rate of convergence appearing in the long-time behavior of viscosity solutions of the Cauchy problem for the Hamilton–Jacobi equation ut(x,t)+ax ·Du(x,t)+b|Du(x,t)|2=f(x)   in \mathbb Rn×(0,￥),u_t(x,t)+\alpha x \cdot Du(x,t)+\beta|Du(x,t)|^2=f(x)\quad{\rm{in}}\,{{\mathbb R}^n}\times(0,\infty),      19. Highly time-oscillating solutions for very fast diffusion equations      Juan Luis V��zquez  Michael Winkler 《Journal of Evolution Equations》2011,11(3):725-742 This work is concerned with the fast diffusion equation ut = ?·(um-1 ?u)        (*) u_t = \nabla \cdot \big(u^{m-1} \nabla u\big) \qquad (\star)      20. Nontangential Limits and Fatou-Type Theorems on Post-Critically Finite Self-Similar Sets      Ricardo A. Sáenz 《Journal of Fourier Analysis and Applications》2012,18(2):240-265 In this paper we study the boundary limit properties of harmonic functions on ℝ+×K, the solutions u(t,x) to the Poisson equation \frac?2 u?t2 + Du = 0,\frac{\partial^2 u}{\partial t^2} + \Delta u = 0,      设为首页 | 免责声明 | 关于勤云 | 加入收藏 Copyright©北京勤云科技发展有限公司  京ICP备09084417号

Non-autonomous stochastic evolution equations and applications to stochastic partial differential equations

In this paper we study the following non-autonomous stochastic evolution equation on a Banach space E: $({\rm SE})\quad \left\{\begin{array}{ll} {\rm d}U(t) = (A(t)U(t) +F(t,U(t)))\,{\rm d}t + B(t,U(t))\,{\rm d}W_H(t), \quad t\in [0,T], \\ U(0) = u_0.\end{array}\right.$ Here, ${(A(t))_{t\in [0,T]}}In this paper we study the following non-autonomous stochastic evolution equation on a Banach space E:

(SE)    {ll dU(t) = (A(t)U(t) +F(t,U(t))) dt + B(t,U(t)) dWH(t),     t ? [0,T], U(0) = u0.({\rm SE})\quad \left\{\begin{array}{ll} {\rm d}U(t) = (A(t)U(t) +F(t,U(t)))\,{\rm d}t + B(t,U(t))\,{\rm d}W_H(t), \quad t\in [0,T], \\ U(0) = u_0.\end{array}\right.      13. Precise Asymptotic Formulas for Semilinear Eigenvalue Problems      T. Shibata 《Annales Henri Poincare》2001,2(4):713-732 . We consider the nonlinear Sturm-Liouville problem¶¶-u"(t) = | u(t) | p-1u(t) - lu(t), t ? I :=(0,1), u(0) = u(1) = 0 -u'(t) = \mid u(t)\mid^{p-1}u(t) - \lambda u(t), t \in I :=(0,1), u(0) = u(1) = 0 ,¶¶ where p > 1 and l ? R \lambda \in {\bf R} is an eigenvalue parameter. To investigate the global L2-bifurcation phenomena, we establish asymptotic formulas for the n-th bifurcation branch l = ln (a) \lambda = \lambda_n (\alpha) with precise remainder term, where a \alpha is the L2 norm of the eigenfunction associated with l \lambda .      14. On the time continuity of entropy solutions      Cl��ment Canc��s  Thierry Gallou?t 《Journal of Evolution Equations》2011,11(1):43-55 We show that any entropy solution u of a convection diffusion equation ?t u + div F(u)-Df(u) = b{\partial_t u + {\rm div} F(u)-\Delta\phi(u) =b} in Ω × (0, T) belongs to C([0,T),L1loc(W)){C([0,T),L^1_{\rm loc}({\Omega}))} . The proof does not use the uniqueness of the solution.      15. The Shuddering Pendulum      Stuart S. Antman 《Journal of Nonlinear Science》2011,21(4):595-638 This paper treats the rich mathematical structure of the (dimensionless) equation of motion governing the behavior of an elastically restrained simple pendulum subject to a downward force of magnitude f(t) applied to its bob with $\dot{f}(t)>0$\dot{f}(t)>0 for all t>0 and f(t)→∞ as t→∞: [(q)\ddot]+2n[(q)\dot] +q = f(t)sinq.\ddot{\theta}+2\nu\dot{\theta} +\theta= f(t)\sin\theta.      16. Quenching phenomena for a non-local diffusion equation with a singular absorption      Raúl Ferreira 《Israel Journal of Mathematics》2011,184(1):387-402 In this paper we study the quenching problem for the non-local diffusion equation ut(x,t) = òW J(x - y)u(y,t)dy + ò\mathbbRN\W J(x - y)dy - u(x,t) - lu - p(x,t) {u_t}(x,t) = \int\limits_\Omega {J(x - y)u(y,t)dy + \int\limits_{{\mathbb{R}^N}\backslash \Omega } {J(x - y)dy - u(x,t) - \lambda {u^{ - p}}(x,t)} }      17. Renormalized solution for Stefan type problems: existence and uniqueness      Noureddine Igbida  Karima Sbihi  Petra Wittbold 《NoDEA : Nonlinear Differential Equations and Applications》2010,17(1):69-93 We consider a class of nonlinear degenerate problems of Stefan type: $u_t- \Delta w -\nabla F(u,w)= g(\cdot,u), \ w\in \beta(u)$ where β is a maximal monotone graph in ${\mathbb{R}^2,}We consider a class of nonlinear degenerate problems of Stefan type: ut- Dw -?F(u,w) = g(·,u),  w ? b(u)u_t- \Delta w -\nabla F(u,w)= g(\cdot,u), \ w\in \beta(u)      18. Long-time behavior of solutions to Hamilton–Jacobi equations with quadratic gradient term      Yasuhiro Fujita  Paola Loreti 《NoDEA : Nonlinear Differential Equations and Applications》2009,16(6):771-791 We study a rate of convergence appearing in the long-time behavior of viscosity solutions of the Cauchy problem for the Hamilton–Jacobi equation ut(x,t)+ax ·Du(x,t)+b|Du(x,t)|2=f(x)   in \mathbb Rn×(0,￥),u_t(x,t)+\alpha x \cdot Du(x,t)+\beta|Du(x,t)|^2=f(x)\quad{\rm{in}}\,{{\mathbb R}^n}\times(0,\infty),      19. Highly time-oscillating solutions for very fast diffusion equations      Juan Luis V��zquez  Michael Winkler 《Journal of Evolution Equations》2011,11(3):725-742 This work is concerned with the fast diffusion equation ut = ?·(um-1 ?u)        (*) u_t = \nabla \cdot \big(u^{m-1} \nabla u\big) \qquad (\star)      20. Nontangential Limits and Fatou-Type Theorems on Post-Critically Finite Self-Similar Sets      Ricardo A. Sáenz 《Journal of Fourier Analysis and Applications》2012,18(2):240-265 In this paper we study the boundary limit properties of harmonic functions on ℝ+×K, the solutions u(t,x) to the Poisson equation \frac?2 u?t2 + Du = 0,\frac{\partial^2 u}{\partial t^2} + \Delta u = 0,      设为首页 | 免责声明 | 关于勤云 | 加入收藏 Copyright©北京勤云科技发展有限公司  京ICP备09084417号

Precise Asymptotic Formulas for Semilinear Eigenvalue Problems

. We consider the nonlinear Sturm-Liouville problem¶¶-u"(t) = | u(t) | ^p-1u(t) - lu(t), t ? I :=(0,1), u(0) = u(1) = 0 -u'(t) = \mid u(t)\mid^{p-1}u(t) - \lambda u(t), t \in I :=(0,1), u(0) = u(1) = 0 ,¶¶ where p > 1 and l ? R \lambda \in {\bf R} is an eigenvalue parameter. To investigate the global L²-bifurcation phenomena, we establish asymptotic formulas for the n-th bifurcation branch l = l_n (a) \lambda = \lambda_n (\alpha) with precise remainder term, where a \alpha is the L² norm of the eigenfunction associated with l \lambda .     

On the time continuity of entropy solutions

We show that any entropy solution u of a convection diffusion equation ?_t u + div F(u)-Df(u) = b{\partial_t u + {\rm div} F(u)-\Delta\phi(u) =b} in Ω × (0, T) belongs to C([0,T),L¹_loc(W)){C([0,T),L^1_{\rm loc}({\Omega}))} . The proof does not use the uniqueness of the solution.     

The Shuddering Pendulum

This paper treats the rich mathematical structure of the (dimensionless) equation of motion governing the behavior of an elastically restrained simple pendulum subject to a downward force of magnitude f(t) applied to its bob with $\dot{f}(t)>0$\dot{f}(t)>0 for all t>0 and f(t)→∞ as t→∞:

Quenching phenomena for a non-local diffusion equation with a singular absorption

In this paper we study the quenching problem for the non-local diffusion equation

Renormalized solution for Stefan type problems: existence and uniqueness

We consider a class of nonlinear degenerate problems of Stefan type: $u_t- \Delta w -\nabla F(u,w)= g(\cdot,u), \ w\in \beta(u)$ where β is a maximal monotone graph in ${\mathbb{R}^2,}We consider a class of nonlinear degenerate problems of Stefan type:

ut- Dw -?F(u,w) = g(·,u),  w ? b(u)u_t- \Delta w -\nabla F(u,w)= g(\cdot,u), \ w\in \beta(u)      18. Long-time behavior of solutions to Hamilton–Jacobi equations with quadratic gradient term      Yasuhiro Fujita  Paola Loreti 《NoDEA : Nonlinear Differential Equations and Applications》2009,16(6):771-791 We study a rate of convergence appearing in the long-time behavior of viscosity solutions of the Cauchy problem for the Hamilton–Jacobi equation ut(x,t)+ax ·Du(x,t)+b|Du(x,t)|2=f(x)   in \mathbb Rn×(0,￥),u_t(x,t)+\alpha x \cdot Du(x,t)+\beta|Du(x,t)|^2=f(x)\quad{\rm{in}}\,{{\mathbb R}^n}\times(0,\infty),      19. Highly time-oscillating solutions for very fast diffusion equations      Juan Luis V��zquez  Michael Winkler 《Journal of Evolution Equations》2011,11(3):725-742 This work is concerned with the fast diffusion equation ut = ?·(um-1 ?u)        (*) u_t = \nabla \cdot \big(u^{m-1} \nabla u\big) \qquad (\star)      20. Nontangential Limits and Fatou-Type Theorems on Post-Critically Finite Self-Similar Sets      Ricardo A. Sáenz 《Journal of Fourier Analysis and Applications》2012,18(2):240-265 In this paper we study the boundary limit properties of harmonic functions on ℝ+×K, the solutions u(t,x) to the Poisson equation \frac?2 u?t2 + Du = 0,\frac{\partial^2 u}{\partial t^2} + \Delta u = 0,      设为首页 | 免责声明 | 关于勤云 | 加入收藏 Copyright©北京勤云科技发展有限公司  京ICP备09084417号

Long-time behavior of solutions to Hamilton–Jacobi equations with quadratic gradient term

We study a rate of convergence appearing in the long-time behavior of viscosity solutions of the Cauchy problem for the Hamilton–Jacobi equation

Highly time-oscillating solutions for very fast diffusion equations

This work is concerned with the fast diffusion equation

Nontangential Limits and Fatou-Type Theorems on Post-Critically Finite Self-Similar Sets

In this paper we study the boundary limit properties of harmonic functions on ℝ₊×K, the solutions u(t,x) to the Poisson equation