On supercritical problems involving the Laplace operator
| Autor: | Pedro Ubilla, Rodrigo Clemente, João Marcos do Ó |
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| Rok vydání: | 2020 |
| Předmět: |
Unit sphere
General Mathematics Mathematical analysis Mathematics::Analysis of PDEs Zero (complex analysis) Type (model theory) 01 natural sciences Domain (mathematical analysis) Supercritical fluid 010305 fluids & plasmas symbols.namesake Dirichlet boundary condition 0103 physical sciences symbols 010306 general physics Laplace operator Complement (set theory) Mathematics |
| Zdroj: | Proceedings of the Royal Society of Edinburgh: Section A Mathematics. 151:187-201 |
| ISSN: | 1473-7124 0308-2105 |
| DOI: | 10.1017/prm.2020.9 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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