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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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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Three solutions for fractional elliptic systems involving ψ-Hilfer operator
Boundary Value ProblemsIn this paper, using variational methods introduced in the previous study on fractional elliptic systems, we prove the existence of at least three weak solutions for an elliptic nonlinear system with a p-Laplacian ψ-Hilfer operator.
Rafik Guefaifia +2 more
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A note on the variational structure of an elliptic system involving critical Sobolev exponent [PDF]
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 [PDF]
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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Elliptic methods for solving the linearized field equations of causal variational principles [PDF]
Calculus of Variations and Partial Differential Equations, 2021 The existence theory is developed for solutions of the inhomogeneous linearized field equations for causal variational principles. These equations are formulated weakly with an integral operator which is shown to be bounded and symmetric on a Hilbert ...
F. Finster, Magdalena Lottner
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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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A priori bounds and positive solutions for non-variational fractional elliptic systems [PDF]
Differential and Integral Equations, 2014 In this paper we study strongly coupled elliptic systems in non-variational form involving fractional Laplace operators. We prove Liouville type theorems and, by mean of the blow-up method, we establish a priori bounds of positive solutions for ...
E. Leite, Marcos Montenegro
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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 +2 more
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Multiple solutions for critical nonhomogeneous elliptic systems in noncontractible domain
Mathematical methods in the applied sciences, 2020 The paper is concerned with multiple solutions of a nonhomogeneous elliptic system with Sobolev critical exponent over a noncontractible domain, precisely, a smooth bounded annular domain.
Xueliang Duan +2 more
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