Displaying similar documents to “Stability results for some nonlinear elliptic equations involving the p-Laplacian with critical Sobolev growth”

On the Neumann problem for an elliptic system of equations involving the critical Sobolev exponent

J. Chabrowski, Jianfu Yang (2001)

Colloquium Mathematicae

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We consider the Neumann problem for an elliptic system of two equations involving the critical Sobolev nonlinearity. Our main objective is to study the effect of the coefficient of the critical Sobolev nonlinearity on the existence and nonexistence of least energy solutions. As a by-product we obtain a new weighted Sobolev inequality.

On elliptic systems pertaining to the Schrödinger equation

J. Chabrowski, E. Tonkes (2003)

Annales Polonici Mathematici

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We discuss the existence of solutions for a system of elliptic equations involving a coupling nonlinearity containing a critical and subcritical Sobolev exponent. We establish the existence of ground state solutions. The concentration of solutions is also established as a parameter λ becomes large.

On some nonlinear elliptic systems with coercive perturbation in R.

Said El Manouni, Abdelfattah Touzani (2003)

Revista Matemática Complutense

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A nonlinear elliptic system involving the p-Laplacian is considered in the whole R. Existence of nontrivial solutions is obtained by applying critical point theory; also a regularity result is established.

Existence of a nontrival solution for Dirichlet problem involving p(x)-Laplacian

Sylwia Barnaś (2014)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

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In this paper we study the nonlinear Dirichlet problem involving p(x)-Laplacian (hemivariational inequality) with nonsmooth potential. By using nonsmooth critical point theory for locally Lipschitz functionals due to Chang [6] and the properties of variational Sobolev spaces, we establish conditions which ensure the existence of solution for our problem.

Direct and Reverse Gagliardo-Nirenberg Inequalities from Logarithmic Sobolev Inequalities

Matteo Bonforte, Gabriele Grillo (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

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We investigate the connection between certain logarithmic Sobolev inequalities and generalizations of Gagliardo-Nirenberg inequalities. A similar connection holds between reverse logarithmic Sobolev inequalities and a new class of reverse Gagliardo-Nirenberg inequalities.

On the p-biharmonic operator with critical Sobolev exponent

Abdelouahed El Khalil, My Driss Morchid Alaoui, Abdelfattah Touzani (2014)

Applicationes Mathematicae

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We study the existence of solutions for a p-biharmonic problem with a critical Sobolev exponent and Navier boundary conditions, using variational arguments. We establish the existence of a precise interval of parameters for which our problem admits a nontrivial solution.