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Existence and Multiplicity of solutions for a quasilinear elliptic system on unbounded domains involving nonlinear boundary conditions 下载免费PDF全文
Somayeh Khademloo Ghasem Alizadeh Afrouzi Jiafa Xu 《Journal of Applied Analysis & Computation》2020,10(3):1094-1106
We prove two existence results for the nonlinear elliptic boundary value system involving $p$-Laplacian over an unbounded domain in $R^N$ with noncompact boundary. The proofs are based on variational methods applied to weighted spaces. 相似文献
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N. Mavinga 《Journal of Differential Equations》2010,248(5):1212-1229
We study the solvability of nonlinear second order elliptic partial differential equations with nonlinear boundary conditions. We introduce the notion of “eigenvalue-lines” in the plane; these eigenvalue-lines join each Steklov eigenvalue to the first eigenvalue of the Neumann problem with homogeneous boundary condition. We prove existence results when the nonlinearities involved asymptotically stay, in some sense, below the first eigenvalue-lines or in a quadrilateral region (depicted in Fig. 1) enclosed by two consecutive eigenvalue-lines. As a special case we derive the so-called nonresonance results below the first Steklov eigenvalue as well as between two consecutive Steklov eigenvalues. The case in which the eigenvalue-lines join each Neumann eigenvalue to the first Steklov eigenvalue is also considered. Our method of proof is variational and relies mainly on minimax methods in critical point theory. 相似文献
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Gennaro Infante Paolamaria Pietramala 《Mathematical Methods in the Applied Sciences》2014,37(14):2080-2090
Using the theory of fixed point index, we discuss the existence and multiplicity of nonnegative solutions of a wide class of boundary value problems with coupled nonlinear boundary conditions. Our approach is fairly general and covers a variety of situations. We illustrate in an example that all the constants that occur in our theory can be computed. Copyright © 2013 John Wiley & Sons, Ltd. 相似文献
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K.J. Brown 《Journal of Mathematical Analysis and Applications》2008,337(2):1326-1336
In this paper, we study the combined effect of concave and convex nonlinearities on the number of solutions for a semilinear elliptic system (Eλ,μ) involving nonlinear boundary condition and sign-changing weight function. With the help of the Nehari manifold, we prove that the system has at least two nontrivial nonnegative solutions when the pair of the parameters (λ,μ) belongs to a certain subset of R2. 相似文献
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C. V. Pao 《Proceedings of the American Mathematical Society》2002,130(4):1079-1086
The aim of this paper is to show the existence and uniqueness of a solution for a system of time-delayed parabolic equations with coupled nonlinear boundary conditions. The time delays are of discrete type which may appear in the reaction function as well as in the boundary function. The approach to the problem is by the method of upper and lower solutions for nonquasimonotone functions.
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Existence of periodic solutions of nonlinear systems with nonlinear boundary conditions 总被引:1,自引:0,他引:1
In this paper we consider the periodic solutions of nonlinear parabolic systems with nonlinear boundary conditions. By constructing the Poincare operator, we obtain the existence of
-periodic weak solutions under some reasonable assumptions. 相似文献
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Miloslav Foistauer Karel Najzar Vcronika Sobotíková 《Numerical Functional Analysis & Optimization》2013,34(9-10):835-851
The paper is concerned with the study of an elliptic boundary value problem with a nonlinear Newton boundary condition. The existence and uniqueness of the solution of the continuous pioblem is a consequence of the monotone operator theory. The main attention is paid to the investigation of the finite element approximation using numeriral integration for the evaluation of boundary integrals. The error estimates for the solution of the discrete finite element problem are derived 相似文献
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研究了一类具非线性边值条件的非线性方程的奇摄动问题,运用合成展开法构造了问题的形式渐近解,并用微分不等式理论证明了所得渐近解的一致有效性. 相似文献
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Guochun WEN Zuoliang XU Department of Mathematics Peking University Beijing China Institute of Computational Mathematics Scientific/Engineering Computing Chinese Academy of Sciences Beijing China 《Communications in Nonlinear Science & Numerical Simulation》2001,6(2):93-96
1 Problem formulation Let Q be a bounded multiply connected domain in RN and the boundary OQ E C2. W6consider the nonlinear elliptic system of second order equationsUnder certain conditions, system (1) can be reduced to the formwhere u = (ul,' t u.), Da = (u..), DZu = (u:..,), andSuppose that (1) (or (2)) satisfiesCondition C For arbitrary functions u'(x), u'(z) E Cd(~) n W::(Q), Fk(x,u,Du,DZu)(k = 1,' I m) satisfy the conditionswhere 0 < g < 1, u == al - u2, and al:), bit), of*),… 相似文献
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Mo Jiaqi Zhang Weijiang Chen Xianfeng 《高校应用数学学报(英文版)》2007,22(4):421-424
The solvability of nonlinear elliptic equation with boundary perturbation is consid- ered.The perturbed solution of original problem is obtained and the uniformly valid expansion of solution is proved. 相似文献
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FengQuan Li 《中国科学 数学(英文版)》2014,57(9):1891-1910
In this paper, we study the very weak solutions to some nonlinear elliptic systems with right-hand side integrable data with respect to the distance to the boundary. Firstly, we study the existence of the approximate solutions. Secondly, a priori estimates are given in the framework of weighted spaces. Finally, we prove the existence, uniqueness and regularity of the very weak solutions. 相似文献
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王明新 《中国科学A辑(英文版)》2003,46(2):169-175
This paper deals with the blow-up rate estimates of positive solutions for systems of heat equations with nonlinear boundary conditions. The upper and lower bounds of blow-up rate are obtained. 相似文献
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We prove existence and uniqueness results for non-linear elliptic equations with lower order terms, L1 data, and mixed boundary conditions that include as particular cases the Dirichlet and the Neumann problems.
Mathematics Subject Classification (2000) 35J25, 35D05, 35J70, 35J60 相似文献
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We report on a result of upper-lower solutions for nonlinear elliptic systems without the assumption of quasi-monotonicity. An application is described involving the existence of positive steady states of a certain interaction system arising in biology and medical sciences. 相似文献
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Miglena Koleva Lubin Vulkov 《Numerical Methods for Partial Differential Equations》2007,23(2):379-399
The numerical solution of the heat equation in unbounded domains (for a 1D problem‐semi‐infinite line and for a 2D one semi‐infinite strip) is considered. The artificial boundaries are introduced and the exact artificial boundary conditions are derived. The original problems are transformed into problems on finite domains. The space semi‐discretization by finite element method and the full approximation by the implicit‐explicit Euler's method are presented. The solvability of the full discretization schemes is analyzed. Computational examples demonstrate the accuracy and the efficiency of the algorithms. Also, the behavior of blowing up solutions is examined numerically. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 379–399, 2007 相似文献
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