共查询到20条相似文献,搜索用时 31 毫秒
1.
Bing Liu 《Journal of Mathematical Analysis and Applications》2005,309(1):313-321
With the help of the coincidence degree continuation theorem, the existence of periodic solutions of a nonlinear second-order differential equation with deviating argument
x″(t)+f1(x(t))x′(t)+f2(x(t))(x′(t))2+g(x(t−τ(t)))=0, 相似文献
2.
Aubrey Truman 《Journal of Functional Analysis》2006,238(2):612-635
In this paper we study the initial problem for a stochastic nonlinear equation arising from 1D integro-differential scalar conservation laws. The equation is driven by Lévy space-time white noise in the following form:
(t∂−A)u+x∂q(u)=f(u)+g(u)Ft,x 相似文献
3.
O. Yu. Khachay 《Differential Equations》2008,44(2):282-285
We consider the Cauchy problem for the nonlinear differential equation where ? > 0 is a small parameter, f(x, u) ∈ C ∞ ([0, d] × ?), R 0 > 0, and the following conditions are satisfied: f(x, u) = x ? u p + O(x 2 + |xu| + |u|p+1) as x, u → 0, where p ∈ ? \ {1} f(x, 0) > 0 for x > 0; f u 2(x, u) < 0 for (x, u) ∈ [0, d] × (0, + ∞); Σ 0 +∞ f u 2(x, u) du = ?∞. We construct three asymptotic expansions (external, internal, and intermediate) and prove that the matched asymptotic expansion approximates the solution uniformly on the entire interval [0, d].
相似文献
$$\varepsilon \frac{{du}}{{dx}} = f(x,u),u(0,\varepsilon ) = R_0 ,$$
4.
Fu Zhang 《Journal of Differential Equations》2004,205(1):77-155
We establish the existence of standing waves with one pulse, multiple spikes and transition layers in the nonlinear reaction-diffusion system
ut=f(u,w)+uxx,wt=?2g(u,w)+wxx,x∈R, 相似文献
5.
Matteo Franca 《Journal of Differential Equations》2010,248(11):2629-2656
We consider the following equation
Δpu(x)+f(u,|x|)=0, 相似文献
6.
João Marcos do Ó Everaldo Medeiros 《Journal of Mathematical Analysis and Applications》2008,345(1):286-304
In this paper we study a class of nonhomogeneous Schrödinger equations
−Δu+V(x)u=f(u)+h(x) 相似文献
7.
We study generalized equations of the following form: (render) where f is Fréchet differentiable in a neighborhood of a solution x* of (*) and g is Fréchet differentiable at x* and where F is a set-valued map acting in Banach spaces. We prove the existence of a sequence (xk) satisfying which is super-linearly convergent to a solution of (*). We also present other versions of this iterative procedure that have superlinear and quadratic convergence, respectively. 相似文献
0f(x)+g(x)+F(x),
8.
We study the convergence and decay rate to equilibrium of bounded solutions of the quasilinear parabolic equation
ut−diva(x,∇u)+f(x,u)=0 相似文献
9.
Gian-Luigi Forti Justyna Sikorska 《Nonlinear Analysis: Theory, Methods & Applications》2011,74(2):343-350
We study the stability of the Drygas functional equation:
g(xy)+g(xy−1)=2g(x)+g(y)+g(y−1) 相似文献
10.
Gwang Hui Kim 《Journal of Mathematical Analysis and Applications》2007,325(1):237-248
The aim of this paper is to study the stability problem of the d'Alembert type and Jensen type functional equations:
f(x+y)+f(x+σy)=2g(x)f(y), 相似文献
11.
We establish propagation and spreading properties for nonnegative solutions of nonhomogeneous reaction-diffusion equations of the type:
t∂u−∇⋅(A(t,x)∇u)+q(t,x)⋅∇u=f(t,x,u) 相似文献
12.
Abbas Najati 《Journal of Mathematical Analysis and Applications》2008,337(1):399-415
In this paper we establish the general solution of the functional equation
f(2x+y)+f(2x−y)=f(x+y)+f(x−y)+2f(2x)−2f(x) 相似文献
13.
Kyung Joong Kim 《Applied mathematics and computation》2011,217(19):7703-7717
We call attention to the entire errors which result when frequency-dependent interpolation formulas are utilized to approximate oscillatory functions f(x) at some x on the domain of interest with a frequency ω of the form,
f(x)=f1(x)cos(ωx)+f2(x)sin(ωx), 相似文献
14.
The properties of the root functions are studied for an arbitrary operator generated in L 2(?1, 1) by the operation with involution of the form Lu = ?u″(x)+αu″(?x)+q(x)u(x)+ qν(x)u(ν(x)), where α ∈ (?1, 1), ν(x) is an absolutely continuous involution of the segment [?1, 1] and the coefficients q(x) and qν(x) are summable functions on (?1, 1). Necessary and sufficient conditions are obtained for the unconditional basis property in L 2(?1, 1) for the system of the root functions of the operator. 相似文献
15.
We consider the quasilinear Schrödinger equations of the form ?ε2Δu + V(x)u ? ε2Δ(u2)u = g(u), x∈ RN, where ε > 0 is a small parameter, the nonlinearity g(u) ∈ C1(R) is an odd function with subcritical growth and V(x) is a positive Hölder continuous function which is bounded from below, away from zero, and infΛV(x) < inf?ΛV(x) for some open bounded subset Λ of RN. We prove that there is an ε0 > 0 such that for all ε ∈ (0, ε0], the above mentioned problem possesses a sign-changing solution uε which exhibits concentration profile around the local minimum point of V(x) as ε → 0+. 相似文献
16.
In this paper, the Fokas unified method is used to analyze the initial-boundary value for the Chen- Lee-Liu equation on the half line (?∞, 0] with decaying initial value. Assuming that the solution u(x, t) exists, we show that it can be represented in terms of the solution of a matrix Riemann-Hilbert problem formulated in the plane of the complex spectral parameter λ. The jump matrix has explicit (x, t) dependence and is given in terms of the spectral functions {a(λ), b(λ)} and {A(λ), B(λ)}, which are obtained from the initial data u0(x) = u(x, 0) and the boundary data g0(t) = u(0, t), g1(t) = ux(0, t), respectively. The spectral functions are not independent, but satisfy a so-called global relation.
相似文献
$i{\partial _t}u + {\partial_{xx}u - i |u{|^2}{\partial _x}u = 0}$
17.
Young-Su Lee Soon-Yeong Chung 《Journal of Mathematical Analysis and Applications》2007,336(1):101-110
In this paper, we consider the general solution of quadratic functional equation
f(ax+y)+f(ax−y)=f(x+y)+f(x−y)+2(a2−1)f(x) 相似文献
18.
Jae-Hyeong Bae 《Applied mathematics and computation》2010,216(1):87-307
For each n=1,2,3, we obtain the general solution and the stability of the functional equation
f(2x+y)+f(2x-y)=2n-2[f(x+y)+f(x-y)+6f(x)]. 相似文献
19.
Abbas Najati 《Journal of Mathematical Analysis and Applications》2008,340(1):569-574
In this paper, we prove the generalized Hyers-Ulam stability for the following quartic functional equation
f(2x+y)+f(2x−y)=4f(x+y)+4f(x−y)+24f(x)−6f(y). 相似文献
20.
In this paper, we study the existence, uniqueness and asymptotic stability of travelling wavefronts of the following equation:
ut(x,t)=D[u(x+1,t)+u(x-1,t)-2u(x,t)]-du(x,t)+b(u(x,t-r)), 相似文献