共查询到20条相似文献,搜索用时 78 毫秒
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We study the following nonlinear boundary value problem with nonhomogeneous multi-point boundary condition
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Sufficient conditions are given for the existence of solutions of the following nonlinear boundary value problem with nonhomogeneous multi-point boundary condition We prove that the whole plane is divided by a “continuous decreasing curve” Γ into two disjoint connected regions ΛE and ΛN such that the above problem has at least one solution for (λ1,λ2)Γ, has at least two solutions for (λ1,λ2)ΛEΓ, and has no solution for (λ1,λ2)ΛN. We also find explicit subregions of ΛE where the above problem has at least two solutions and two positive solutions, respectively. 相似文献
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《Journal of Computational and Applied Mathematics》2005,174(2):315-327
We develop a new method of lower and upper solutions for a fourth-order nonlinear boundary value problem where the differential equation has dependence on all lower-order derivatives. Our boundary conditions are nonlinear. We will assume the functions that define the nonlinear boundary conditions are either monotone or nonmonotone. As a result we obtain existence principles which improve recent results in the literature. 相似文献
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In this paper, the upper and lower solution method and Schauder’s fixed point theorem are employed in the study of boundary value problems for a class of second-order impulsive ordinary differential equations with nonlinear boundary conditions. We prove the existence of solutions to the problem under the assumption that there exist lower and upper solutions associated with the problem. 相似文献
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We study the convergence of the solutions of the Dirichlet problem associated to a degenerate nonlinear higher-order elliptic equations in divergence form in variables domains, to a limit solution of the same type problem in a fixed domain, following the methods of the asymptotic expansion developed by Skrypnik [Methods for Analysis of Nonlinear Elliptic Boundary Value Problems, AMS, Providence, RI, 1994] modified to weighted higher-order case. 相似文献
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We study nth order boundary value problems with a nonlinear term f(t,x) subject to nonhomogeneous multi-point boundary conditions. Criteria for the existence of positive solutions of such problems are established. Conditions are determined by the relationship between the behavior of f(t,x)/x near 0 and ∞ when compared with the smallest positive characteristic value of an associated linear integral operator. This work improves and extends some recent results in the literature for the second order problems. The results are illustrated with examples. 相似文献
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Differential inequality method, bounding function method and topological degree are applied to obtain the existence criterions of at least one solution for the general fourth-order differential equations under nonlinear boundary conditions, and many existing results are complemented. 相似文献
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Tamás Kurics 《Journal of Computational and Applied Mathematics》2010,235(2):437-449
The numerical solution of linear elliptic partial differential equations often involves finite element discretization, where the discretized system is usually solved by some conjugate gradient method. The crucial point in the solution of the obtained discretized system is a reliable preconditioning, that is to keep the condition number of the systems under control, no matter how the mesh parameter is chosen. The PCG method is applied to solving convection-diffusion equations with nonhomogeneous mixed boundary conditions. Using the approach of equivalent and compact-equivalent operators in Hilbert space, it is shown that for a wide class of elliptic problems the superlinear convergence of the obtained preconditioned CGM is mesh independent under FEM discretization. 相似文献
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This note deals with some boundary value problems in a self-similar ramified domain of , with a fractal boundary. The partial differential equation is Laplace's equation, and there are nonhomogeneous generalized Neumann boundary conditions on the fractal boundary. We propose a multiscale strategy for approximating the restriction of the solutions to simple subdomains. This strategy is based on transparent boundary conditions and on a wavelet expansion of the Neumann datum. To cite this article: Y. Achdou, N. Tchou, C. R. Acad. Sci. Paris, Ser. I 342 (2006). 相似文献
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A constructive approach to the determination of an approximate solution of a boundary value problem with nonlinear boundary conditions g[z (0), z (T)]=0 is proposed. Existence of the exact solution is proved, and error estimates for the constructed approximate solution are provided.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 42, No. 7, pp. 951–957, July, 1990. 相似文献
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Alexandre N. Carvalho German Lozada-Cruz 《Journal of Mathematical Analysis and Applications》2007,325(2):1216-1239
We obtain existence of asymptotically stable nonconstant equilibrium solutions for semilinear parabolic equations with nonlinear boundary conditions on small domains connected by thin channels. We prove the convergence of eigenvalues and eigenfunctions of the Laplace operator in such domains. This information is used to show that the asymptotic dynamics of the heat equation in this domain is equivalent to the asymptotic dynamics of a system of two ordinary differential equations diffusively (weakly) coupled. The main tools employed are the invariant manifold theory and a uniform trace theorem. 相似文献
14.
We construct and study self-adjoint operators corresponding to problems mentioned in the title. We describe a correlation between domains of definition of fractional powers of these operators and Sobolev spaces. We state new results on the solvability of several problems for nonlinear parabolic equations which have not yet been studied.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 3, pp. 374–381, March, 1991. 相似文献
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We construct and study self-adjoint operators corresponding to problems mentioned in the title. We describe a correlation between domains of definition of fractional powers of these operators and Sobolev spaces. We state new results on the solvability of several problems for nonlinear parabolic equations which have not yet been studied.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 3, pp. 374–381, March, 1991. 相似文献
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Giuseppe Maria Coclite Gisèle Ruiz Goldstein Jerome A. Goldstein 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2013,64(3):733-753
Of concern is the nonlinear hyperbolic problem with nonlinear dynamic boundary conditions $$\left\{ \begin{array}{lll} u_{tt} ={\rm div} (\mathcal{A} \nabla u)-\gamma (x,u_t), && \quad {\rm in} \; (0, \infty) \times \Omega,\\ u(0, \cdot)=f, \, u_t(0,\cdot)=g, && \quad {\rm in}\; \Omega, \\ u_{tt} + \beta \partial^ \mathcal{A}_\nu u+c(x)u+ \delta (x,u_t)-q \beta \Lambda_{\rm LB} u=0,&& \quad {\rm on} \;(0, \infty ) \times \partial \Omega . \end{array}\right. $$ for t ≥ 0 and ${x \in \Omega \subset \mathbb{R}^N}$ ; the last equation holds on the boundary ?Ω. Here ${\mathcal{A}= \{a_{ij}(x)\}_{ij}}$ is a real, hermitian, uniformly positive definite N × N matrix; ${\beta \in C(\partial \Omega)}$ , with β > 0; ${\gamma:\Omega \times \mathbb{R} \to \mathbb{R}; \delta:\partial \Omega \times \mathbb{R} \to \mathbb{R}; \,c:\partial \Omega \to \mathbb{R}; \, q \ge 0, \Lambda_{\rm LB}}$ is the Laplace–Beltrami operator on ?Ω, and ${\partial^\mathcal{A}_\nu u}$ is the conormal derivative of u with respect to ${\mathcal{A}}$ ; everything is sufficiently regular. We prove explicit stability estimates of the solution u with respect to the coefficients ${\mathcal{A},\,\beta,\,\gamma,\,\delta,\,c,\,q}$ , and the initial conditions f, g. Our arguments cover the singular case of a problem with q = 0 which is approximated by problems with positive q. 相似文献
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We establish necessary and sufficient conditions for the existence of solutions of weakly nonlinear degenerate boundary-value
problems for systems of ordinary differential equations with a Noetherian operator in the linear part. We propose a convergent
iterative procedure for finding solutions and establish the relationship between necessary and sufficient conditions. 相似文献
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Second-order nonlinear singular Sturm-Liouville problems with integral boundary conditions 总被引:1,自引:0,他引:1
This paper is concerned with the second-order singular Sturm-Liouville integral boundary value problems
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Giuseppe M. Coclite Gisèle R. Goldstein Jerome A. Goldstein 《Journal of Differential Equations》2009,246(6):2434-3971
Of concern is the nonlinear uniformly parabolic problem