Weighted critical exponents of Sobolev-type embeddings for radial functions [PDF]
Advanced Nonlinear Studies, 2022 In this article, we prove the upper weighted critical exponents for some embeddings from weighted Sobolev spaces of radial functions into weighted Lebesgue spaces. We also consider the lower critical exponent for certain embedding.
Su Jiabao, Wang Cong
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On p-Laplace Equations with Singular Nonlinearities and Critical Sobolev Exponent [PDF]
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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Existence and multiplicity of solutions for Kirchhof-type problems with Sobolev–Hardy critical exponent [PDF]
Boundary Value Problems, 2021 In this paper, we discuss a class of Kirchhof-type elliptic boundary value problem with Sobolev–Hardy critical exponent and apply the variational method to obtain one positive solution and two nontrivial solutions to the problem under certain conditions.
Hongsen Fan, Zhiying Deng
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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 Hamiltonian systems with critical Sobolev exponents [PDF]
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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Multiple solutions for weighted Kirchhoff equations involving critical Hardy-Sobolev exponent [PDF]
Advances in Nonlinear Analysis, 2020 In this article, we consider a class of Kirchhoff equations with critical Hardy-Sobolev exponent and indefinite nonlinearity, which has not been studied in the literature. We prove very nicely that this equation has at least two solutions in ℝ3. And some
Shen Zupei, Yu Jianshe
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Bifurcation of positive solutions for a semilinear equation with critical Sobolev exponent
Electronic Journal of Differential Equations, 2006 In this note we consider bifurcation of positive solutions to the semilinear elliptic boundary-value problem with critical Sobolev exponent $$displaylines{ -Delta u = lambda u - alpha u^p+ u^{2^*-1}, quad u >0 , quad hbox{in } Omega,cr u=0, quad hbox ...
Yuanji Cheng
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Sobolev Critical Exponents of Rational Homotopy Groups [PDF]
Pure and Applied Mathematics Quarterly, 2007 Tristan Rivière
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On a singular nonlinear Neumann problem [PDF]
Opuscula Mathematica, 2014 We investigate the solvability of the Neumann problem involving two critical exponents: Sobolev and Hardy-Sobolev. We establish the existence of a solution in three cases: \(\text{(i)}\;\ 2\lt p+1\lt 2^*(s),\) \(\text{(ii)}\;\ p+1=2^*(s)\) and \(\text ...
Jan Chabrowski
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