Existence of non-negative solutions for semilinear elliptic systems via variational methods
Nonlinear Analysis, 2012 In this paper we consider a semilinear elliptic system with nonlinearities, indefinite weight functions and critical growth terms in bounded domains. The existence result of nontrivial nonnegative solutions is obtained by variational methods.
Somayeh Khademloo, Shapur Heidarkhani
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Variational Methods in the Study of Inequality Problems for Nonlinear Elliptic Systems with Lack of Compactness [PDF]
Real Analysis Exchange, 2008 We establish the existence of an entire weak solution for a class of stationary Schrodinger systems with subcritical discontinuous nonlinearities and lower bounded potentials that blow-up at infinity. The proof relies on Chang's version of the Mountain Pass Lemma for locally Lipschitz functionals.
Teodora-Liliana Dinu
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Infinitely many solutions for a class of quasilinear two-point boundary value systems [PDF]
Electronic Journal of Qualitative Theory of Differential Equations, 2015 The existence of infinitely many solutions for a class of Dirichlet quasilinear elliptic systems is established. The approach is based on variational methods.
Giuseppina D'Aguì +2 more
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On finding bifurcations for non-variational elliptic systems by the extended quotients method [PDF]
We develop a novel method for finding bifurcations for nonlinear systems of equations based on directly finding bifurcations through saddle points of extended quotients. The method is applied to find the saddle-node bifurcation point for elliptic equations with the nonlinearity of the general convex-concave type.
Yavdat Il’yasov
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A variational method for solving quasilinear elliptic systems involving symmetric multi-polar potentials [PDF]
Differential Equations & Applications, 2020 Ali Jabar Rashidi, Mohsen Shekarbaigi
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Existence of solutions for a non-variational system of elliptic PDE's via topological methods
Electronic Journal of Differential Equations, 2016 In this article, we prove the existence of solutions for a non-variational system of elliptic PDE's. Also we study a system of bi-Laplacian equations with two nonlinearities and without variational assumptions. First, we prove a priori solution estimates, and then we use fixed point theory, to deduce the existence of solutions.
Fethi Soltani, Habib Yazidi
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Nonlocal fractional p(⋅)-Kirchhoff systems with variable-order: Two and three solutions
AIMS Mathematics, 2021 In this article, we consider the following nonlocal fractional Kirchhoff-type elliptic systems $ \begin{equation*} \left\{\begin{array}{l} -M_{1}\left(\int_{\mathbb{R}^{N}\times\mathbb{R}^{N}}\frac{|\eta(x)-\eta(y)|^{^{p(x, y)}}}{p(x, y)|x-y|^{N+p(
Weichun Bu +3 more
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Multiple solutions for a class of nonlocal quasilinear elliptic systems in Orlicz–Sobolev spaces
Boundary Value Problems, 2021 In this paper, we study some results on the existence and multiplicity of solutions for a class of nonlocal quasilinear elliptic systems. In fact, we prove the existence of precise intervals of positive parameters such that the problem admits multiple ...
S. Heidari, A. Razani
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EXISTENCE OF THE SOLUTIONS FOR THE SINGULAR POTENTIAL ELLIPTIC SYSTEM [PDF]
Korean Journal of Mathematics, 2012 Using the direct method, we prove the Hyers-Ulam stability of the orthogonally additive-quartic functional equation $f (2x + y) + f (2x − y) = 4f (x + y) + 4f (x − y)+ 10f (x) + 14f (−x) − 3f (y) − 3f (−y)$ for all x, y with x ⊥ y, in non-Archimedean Banach spaces. Here ⊥ is the orthogonality in the sense of R atz.
Hyunju Lee +4 more
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Optimal Lipschitz criteria and local estimates for non-uniformly elliptic problems [PDF]
, 2018 We report on new techniques and results in the regularity theory of general non-uniformly elliptic variational integrals. By means of a new potential theoretic approach we reproduce, in the non-uniformly elliptic setting, the optimal criteria for ...
Beck, Lisa, Mingione, Giuseppe
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