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Problem With Critical Sobolev Exponent and With Potential on SN [PDF]
Journal of Applied MathematicsWe consider the equation −divSNqx∇Snu=u2∗−1,u>0 in D’, u=0 on D′, where D′ is a geodesic ball with radius θ1, centered at the north pole, on SN, N≥4, and q is a positive continuous function.
Walid Refai, Habib Yazidi
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The Existence Result for a p-Kirchhoff-Type Problem Involving Critical Sobolev Exponent
Journal of Function Spaces, 2023 In this paper, by using the mountain pass theorem and the concentration compactness principle, we prove the existence of a positive solution for a p-Kirchhoff-type problem with critical Sobolev exponent.
Hayat Benchira +3 more
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Fractional Laplacian equations with critical Sobolev exponent [PDF]
Revista Matemática Complutense, 2015 In this paper we complete the study of the following elliptic equation driven by a general non-local integrodifferential operator $$\mathcal {L}_K$$
Raffaella Servadei, E. Valdinoci
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Inhomogeneous Neumann problem with critical Sobolev exponent [PDF]
Advances in Nonlinear Analysis, 2012 We investigate the solvability of the inhomogeneous Neumann problem involving the critical Sobolev exponent. In particular, we discuss the impact of the shape of the graph of the coefficient of the critical exponent on the existence of a solution.
Chabrowski Jan
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On p-Laplace Equations with Singular Nonlinearities and Critical Sobolev Exponent
Journal of Function Spaces, 2022 In this paper, we deal with p-Laplace equations with singular nonlinearities and critical Sobolev exponent. By using the Nehari manifold, Mountain Pass theorem, and Maximum principle theorem, we prove the existence of at least four distinct nontrivial ...
Mohammed El Mokhtar ould El Mokhtar
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On a semilinear Schrödinger equation with critical Sobolev exponent [PDF]
Proceedings of the American Mathematical Society, 2001 We consider the semilinear Schrodinger equation -Deltau+V(x)u= K(x) \u \ (2*-2 u) + g(x; u), u is an element of W-1,W-2 (R-N), where N greater than or equal to4, V, K, g are periodic in x(j) for 1 less than or equal toj less than or equal toN, K>0, g is of subcritical growth and 0 is in a gap of the spectrum of -Delta +V.
J. Chabrowski, Andrzej Szulkin
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Advanced Nonlinear Studies, 2020 In this paper, we study the existence of ground state solutions for the nonlinear Schrödinger–Bopp–Podolsky system with critical Sobolev ...
Li Lin, Pucci Patrizia, Tang Xianhua
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On Hamiltonian systems with critical Sobolev exponents
Journal of Differential Equations, 2022 26 ...
Angelo guimarães +1 more
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Solutions for the quasi-linear elliptic problems involving the critical Sobolev exponent [PDF]
Journal of Inequalities and Applications, 2017 In this article, we study the existence and multiplicity of positive solutions for the quasi-linear elliptic problems involving critical Sobolev exponent and a Hardy term.
Yanbin Sang, Siman Guo
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On Dirac equation with a potential and critical Sobolev exponent
Communications on Pure and Applied Analysis, 2015 In this paper we consider a critical Dirac equation with a potential on a compact spin manifold. We prove the existence of solutions based on the analysis of the spectrum of Dirac operator with a potential and the dual variational method.
Wenmin Gong, Guangcun Lu
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