Results 1 to 10 of about 546 (190)

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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A variational method for solving quasilinear elliptic systems involving symmetric multi-polar potentials [PDF]

Differential Equations & Applications, 2020
Summary: In this paper, a system of quasilinear elliptic equations is investigated, which involves multiple critical Hardy-Sobolev exponents and symmetric multi-polar potentials. By employing the variational methods and analytic techniques, the relevant best constants are studied and the existence of \((\mathbb{Z}_k \times\mathbb{SO}(N-2))^2 ...
Rashidi, Ali Jabar, Shekarbaigi, Mohsen
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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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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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Existence of solutions for a non-variational system of elliptic PDE's via topological methods

Electronic Journal of Differential Equations, 2016
Summary: 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, Tianqing An, Guoju Ye, Yating Guo   +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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Infinitely many solutions for a class of quasilinear two-point boundary value systems

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, Shapour Heidarkhani, Angela Sciammetta   +2 more
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A note on the variational structure of an elliptic system involving critical Sobolev exponent

Journal of Applied Mathematics, 2003
We consider an elliptic system involving critical growth conditions. We develop a technique of variational methods for elliptic systems. Using the well-known results of maximum principle for systems developed by Fleckinger et al.
Mario Zuluaga
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Nonlinear elliptic systems

Anais da Academia Brasileira de Ciências, 2000
In this paper we treat the question of the existence of solutions of boundary value problems for systems of nonlinear elliptic equations of the form - deltau = f (x, u, v,Ñu,Ñv), - deltav = g(x, u, v, Ñu, Ñv), in omega, We discuss several classes of such
DJAIRO G. DEFIGUEIREDO
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