共查询到20条相似文献,搜索用时 765 毫秒
1.
Yongxiang Li 《Journal of Mathematical Analysis and Applications》2003,282(1):232-240
In this paper the existence results of positive solutions are obtained for second-order boundary value problem
−u″=f(t,u),t∈(0,1),u(0)=u(1)=0, 相似文献
2.
Let a∈C[0,1], b∈C([0,1],(−∞,0]). Let φ1(t) be the unique solution of the linear boundary value problem
u″(t)+a(t)u′(t)+b(t)u(t)=0,t∈(0,1),u(0)=0,u(1)=1. 相似文献
3.
We prove existence and uniqueness of positive solutions for the boundary value problem
(rN−1φ(u′))′=−λrN−1f(u),u′(0)=u(1)=0, 相似文献
4.
This paper investigates the existence and uniqueness of positive and nondecreasing solution for nonlinear boundary value problem with fractional q-derivative where \(D_{q}^{\alpha }\) denotes the Riemann–Liouville q-derivative of order \(\alpha \), \(0<\eta <1\) and \(1-\beta \eta ^{\alpha -3}>0\). Our analysis relies a fixed point theorem in partially ordered sets. An example to illustrate our results is given.
相似文献
$$\begin{aligned}&D_{q}^{\alpha }u(t)+f(t,u(t))=0, \quad {0<t<1, ~3<\alpha \le 4,} \\&u(0)= D_{q}u(0)=D_{q}^{2}u(0)=0, \quad D_{q}^{2}u(1)=\beta D_{q}^{2}u(\eta ), \end{aligned}$$
5.
Stepan Tersian Julia Chaparova 《Journal of Mathematical Analysis and Applications》2002,272(1):223-239
In this paper we study the existence of periodic solutions of the sixth-order equation
uvi+Auiv+Bu″+u−u3=0, 相似文献
6.
Existence of solutions for wave-type hemivariational inequalities with noncoercive viscosity damping
Leszek Gasiński Maciej Smo?ka 《Journal of Mathematical Analysis and Applications》2002,270(1):150-164
In this paper we prove the existence of solutions for a hyperbolic hemivariational inequality of the form
u″+Au′+Bu+∂j(u)∋f, 相似文献
7.
In this paper we study the existence and multiplicity of solutions of the following operator equation in Banach space E:
u=λAu,0<λ<+∞,u∈P?{θ}, 相似文献
8.
We study the positive solution \({u(r,\rho)}\) of the quasilinear elliptic equationThis class of differential operators includes the usual Laplace, m-Laplace, and k-Hessian operators in the space of radial functions. The equation has a singular positive solution u *(r) under certain conditions on \({\alpha}\), \({\beta}\), \({\gamma}\), and p. A generalized Joseph–Lundgren exponent, which we denote by \({p^*_{JL}}\), is obtained. We study the intersection numbers between \({u(r,\rho)}\) and u *(r) and between \({u(r,\rho_0)}\) and \({u(r,\rho_1)}\), and see that \({p^*_{JL}}\) plays an important role. We also determine the bifurcation diagram of the problemThe main technique used in the proofs is a phase plane analysis.
相似文献
$$\begin{cases}r^{-(\gamma-1)}(r^{\alpha}|u^{\prime}|^{\beta-1}u^{\prime})^{\prime}+|u|^{p-1}u=0, & 0 < r < \infty,\\ u(0) = \rho > 0,\ u^{\prime}(0)=0.\end{cases}$$
$$\begin{cases}r^{-(\gamma-1)}(r^{\alpha}|u^{\prime}|^{\beta-1}u^{\prime})^{\prime} + \lambda(u+1)^p=0, & 0 < r < 1,\\ u(r) > 0, & 0 \le r < 1,\\ u^{\prime}(0)=0,\ u(1)=0.\end{cases}$$
9.
In this paper, we consider the obstacle problem for the inhomogeneous p-Laplace equation
$ \text {div}\big(|\nabla u|^{p-2} \nabla u\big)=f\cdot \chi_{ \{u>0\},} 相似文献 10.
Abdulkadir Dogan 《Positivity》2018,22(5):1387-1402
This paper deals with the existence of positive solutions of nonlinear differential equation 相似文献
$$\begin{aligned} u^{\prime \prime }(t)+ a(t) f(u(t) )=0,\quad 0<t <1, \end{aligned}$$ $$\begin{aligned} u(0)=\sum _{i=1}^{m-2} a_i u (\xi _i) ,\quad u^{\prime } (1) = \sum _{i=1}^{m-2} b_i u^{\prime } (\xi _i), \end{aligned}$$ $$\begin{aligned} \displaystyle \inf _{0 \le t \le 1} u(t) \ge \gamma \Vert u\Vert _\infty . \end{aligned}$$ 11.
César E. Torres Ledesma Nemat Nyamoradi 《Journal of Applied Mathematics and Computing》2017,55(1-2):257-278
In the present paper, we deal with the existence and multiplicity of solutions for the following impulsive fractional boundary value problem 相似文献
$$\begin{aligned} {_{t}}D_{T}^{\alpha }\left( \left| {_{0}}D_{t}^{\alpha }u(t)\right| ^{p-2}{_{0}}D_{t}^{\alpha }u(t)\right) + a(t)|u(t)|^{p-2}u(t)= & {} f(t,u(t)),\;\;t\ne t_j,\;\;\hbox {a.e.}\;\;t\in [0,T],\\ \Delta \left( {_{t}}I_{T}^{1-\alpha }\left( \left| {_{0}}D_{t}^{\alpha }u(t_j)\right| ^{p-2}{_{0}}D_{t}^{\alpha }u(t_j)\right) \right)= & {} I_j(u(t_j))\;\;j=1,2,\ldots ,n,\\ u(0)= & {} u(T) = 0. \end{aligned}$$ $$\begin{aligned} \Delta \left( {_{t}}I_{T}^{1-\alpha }\left( \left| {_{0}}D_{t}^{\alpha }u(t_j)\right| ^{p-2}{_{0}}D_{t}^{\alpha }u(t_j)\right) \right)= & {} {_{t}}I_{T}^{1-\alpha }\left( \left| {_{0}}D_{t}^{\alpha }u\left( t_j^+\right) \right| ^{p-2}{_{0}}D_{t}^{\alpha }u\left( t_j^+\right) \right) \\&- {_{t}}I_{T}^{1-\alpha }\left( \left| {_{0}}D_{t}^{\alpha }u(t_j^-)\right| ^{p-2}{_{0}}D_{t}^{\alpha }u\left( t_j^-\right) \right) ,\\ {_{t}}I_{T}^{1-\alpha }\left( \left| {_{0}}D_{t}^{\alpha }u\left( t_j^+\right) \right| ^{p-2}{_{0}}D_{t}^{\alpha }u\left( t_j^+\right) \right)= & {} \lim _{t \rightarrow t_j^+} {_{t}}I_{T}^{1-\alpha }\left( \left| {_{0}}D_{t}^{\alpha }u(t)\right| ^{p-2}{_{0}}D_{t}^{\alpha }u(t)\right) ,\\ {_{t}}I_{T}^{1-\alpha }\left( \left| {_{0}}D_{t}^{\alpha }u(t_j^-)\right| ^{p-2}{_{0}}D_{t}^{\alpha }u(t_j^-)\right)= & {} \lim _{t\rightarrow t_j^-}{_{t}}I_{T}^{1-\alpha }\left( \left| {_{0}}D_{t}^{\alpha }u(t)\right| ^{p-2}{_{0}}D_{t}^{\alpha }u(t)\right) . \end{aligned}$$ 12.
In this paper, we deal with a class of semilinear parabolic problems related to a Hardy inequality with singular weight at the boundary.
More precisely, we consider the problem $$\left\{\begin{array}{l@{\quad}l}u_t-\Delta u=\lambda \frac{u^p}{d^2}&\text{ in }\,\Omega_{T}\equiv\Omega \times (0,T), \\u>0 &\text{ in }\,{\Omega_T}, \\u(x,0)=u_0(x)>0 &\text{ in }\,\Omega, \\u=0 &\text{ on }\partial \Omega \times (0,T),\end{array}\right.$$ (P) We prove that 相似文献
13.
Changfeng Gui Jie Zhang Zhuoran Du 《Journal of Fixed Point Theory and Applications》2017,19(1):363-373
We consider periodic solutions of the following problem associated with the fractional Laplacian 相似文献
$$(-\partial _{xx})^s u(x) + F'(u(x))=0,\quad u(x)=u(x+T),\quad \text{ in } \, \mathbb {R}, $$ 14.
We use the fixed point index theory of condensing mapping in cones discuss the existence of positive solutions for the following boundary value problem of fractional differential equations in a Banach space E 相似文献
$$\begin{aligned} \left\{ \begin{array}{ll} -D^{\,\beta }_{0^{+}}u(t)=f(t,u(t)),\quad t\in J, \\ u(0)=u^{\prime }(0)=\theta ,\quad u(1)=\rho \int _{0}^{1}u(t)dt,\\ \end{array} \right. \end{aligned}$$ 15.
In this paper, we deal with the following nonlinear fractional differential problem in the half-line \({\mathbb{R}^{+}=(0,+ \infty)}\) 相似文献
$$\left\{\begin{array}{l}D^{\alpha }u(x)+f(x,u(x),D^{p}u(x))=0,\quad x \in \mathbb{R}^{+},\\ u(0)=u^{\prime } \left( 0\right) = \cdots =u^{\left( m-2\right) }(0)=0,\end{array}\right.$$ 16.
In this paper we discuss the existence and the global behavior of positive solutions of the following generalized Lane–Emden system of differential equations: 相似文献
$$\begin{aligned} -u''= & {} a(x)u^{\alpha }\,v^{r}\quad \text{ in } (0,1), \\ -v''= & {} b(x)u^{s}\,v^{\beta }\quad \, \text{ in } (0,1), \\ u'(0)= & {} v'(0)=0; \quad \, u(1)=v(1)=0, \end{aligned}$$ 17.
In this paper, we study the existence result for the nonlinear fractional differential equations with p-Laplacian operator 相似文献
$$\left\{\begin{array}{ll}D_{0^+}^{\beta} \phi_p( D_{0^+}^{\alpha} u(t))=f(t,u(t),D_{0^+}^{\alpha}u(t)), \quad t\in(0,1),\\ D_{0^+}^{\alpha}u(0)=D_{0^+}^{\alpha}u(1)=0,\end{array}\right.$$ 18.
In this paper we study the following singular p(x)-Laplacian problem 相似文献
$$\begin{aligned} \left\{ \begin{array}{l@{\quad }l} - \text{ div } \left( |\nabla u|^{p(x)-2} \nabla u\right) =\frac{ \lambda }{u^{\beta (x)}}+u^{q(x)}, &{} \text{ in }\quad \Omega , \\ u>0, &{} \text{ in }\quad \Omega , \\ u=0, &{} \text{ on }\quad \partial \Omega , \end{array}\right. \end{aligned}$$ 19.
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