On the p-biharmonic operator with critical Sobolev exponent

Abdelouahed El Khalil; My Driss Morchid Alaoui; Abdelfattah Touzani

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Multiple solutions for a class of p(x)-Laplacian equations involving the critical exponent

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We study the multiplicity of solutions for a class of p(x)-Laplacian equations involving the critical exponent. Under suitable assumptions, we obtain a sequence of radially symmetric solutions associated with a sequence of positive energies going toward infinity.

On positive solutions of nonlinear elliptic equations involving concave and critical nonlinearities

J. Chabrowski, P. Drábek (2002)

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We study the existence of nonnegative solutions of elliptic equations involving concave and critical Sobolev nonlinearities. Applying various variational principles we obtain the existence of at least two nonnegative solutions.

Critical exponent and minimization problem in $ℝ^{N}$

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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.

A nonexistence theorem for an equation with critical Sobolev exponent in the half space.

H. Berestycki, M. Gross, F. Pacella (1992)

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On multiple solutions of the Neumann problem involving the critical Sobolev exponent

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We consider the Neumann problem involving the critical Sobolev exponent and a nonhomogeneous boundary condition. We establish the existence of two solutions. We use the method of sub- and supersolutions, a local minimization and the mountain-pass principle.