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On supercritical problems involving the Laplace operator
Published online by Cambridge University Press: 27 February 2020
Abstract
We discuss the existence, nonexistence and multiplicity of solutions for a class of elliptic equations in the unit ball with zero Dirichlet boundary conditions involving nonlinearities with supercritical growth. By using Pohozaev type identity we prove a nonexistence result for a class of supercritical problems with variable exponent which allow us to complement the analysis developed in (Calc. Var. (2016) 55:83). Moreover, we establish existence results of positive solutions for semilinear elliptic equations involving nonlinearities which are subcritical at infinity just in a part of the domain, and can be supercritical in a suitable sense.
- Type
- Research Article
- Information
- Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 151 , Issue 1 , February 2021 , pp. 187 - 201
- Copyright
- Copyright © The Author(s) 2020. Published by The Royal Society of Edinburgh
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