A NONEXISTENCE RESULT OF SINGLE PEAKED SOLUTIONS TO A SUPERCRITICAL NONLINEAR PROBLEM

DOI10.1142/S0219199703000951zbMath1066.35035OpenAlexW2071801263MaRDI QIDQ4707469

Massimo Grossi, Olivier Rey, Mohamed Ben Ayed, Khalil O. El Mehdi

Publication date: 7 October 2003

Published in: Communications in Contemporary Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1142/s0219199703000951

zbMATH Keywords

critical Sobolev exponentsemilinear elliptic problemsnonexistence results

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05)

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Multi-bubble solutions for a slightly supercritical elliptic problem in a domain with a small hole ⋮ Qualitative analysis of single peaked solutions for the supercritical Hénon problem ⋮ Construction of solutions of an elliptic PDE with a supercritical exponent nonlinearity using the finite dimensional reduction ⋮ Construction of solutions of an supercritical elliptic PDE in low dimensions ⋮ Boundary clustered layers near the higher critical exponents ⋮ A new perturbation to a critical elliptic problem with a variable exponent ⋮ Nonexistence of interior bubbling solutions for slightly supercritical elliptic problems ⋮ Boundary towers of layers for some supercritical problems ⋮ The effect of linear perturbations on the Yamabe problem ⋮ Radial solutions for the Brezis-Nirenberg problem involving large nonlinearities ⋮ On a biharmonic equation involving slightly supercritical exponent ⋮ A new kind of blowing-up solutions for the Brezis-Nirenberg problem ⋮ On a fourth order elliptic equation with supercritical exponent ⋮ Concentration and multiplicity of solutions for a fourth-order equation with critical nonlinearity ⋮ Supercritical elliptic problem with nonautonomous nonlinearities ⋮ Bubble towers for supercritical semilinear elliptic equations ⋮ Sign changing bubble tower solutions in a slightly subcritical semilinear Dirichlet problem ⋮ Blowing-up solutions for a supercritical elliptic equation ⋮ Finite-dimensional reduction of a supercritical exponent equation ⋮ Nonexistence Results of Sign-changing solutions for a Supercritical Problem of the Scalar Curvature Type ⋮ Concentration Phenomena in a Biharmonic Equation Involving the Critical Sobolev Exponent ⋮ Sign-changing blowing-up solutions for supercritical Bahri-Coron's problem

Cites Work

• Multiplicity of positive solutions of nonlinear elliptic equations with critical Sobolev exponent in some contractible domains
• Proof of two conjectures of H. Brezis and L. A. Peletier
• On a variational problem with lack of compactness: The topological effect of the critical points at infinity
• The role of the Green's function in a nonlinear elliptic equation involving the critical Sobolev exponent
• Nonexistence results for elliptic problems with supercritical nonlinearity in nontrivial domains
• Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth
• A Note on an Equation with Critical Exponent
• On a nonlinear elliptic equation involving the critical sobolev exponent: The effect of the topology of the domain

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