A priori bounds and existence of positive solutions for semilinear elliptic systems
| Autor: | Nsoki Mavinga, Rosa Pardo |
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| Rok vydání: | 2017 |
| Předmět: |
Pure mathematics
Applied Mathematics 010102 general mathematics Mathematical analysis Mathematics::Analysis of PDEs Regular polygon Type (model theory) 01 natural sciences Hyperbola 010101 applied mathematics Sobolev space Bounded function A priori and a posteriori 0101 mathematics Power function Analysis Bifurcation Mathematics |
| Zdroj: | Journal of Mathematical Analysis and Applications. 449:1172-1188 |
| ISSN: | 0022-247X |
| Popis: | We provide a-priori L ∞ bounds for classical positive solutions of semilinear elliptic systems in bounded convex domains when the nonlinearities are below the power functions v p and u q for any ( p , q ) lying on the critical Sobolev hyperbola. Our proof combines moving planes method and Rellich–Pohozaev type identities for systems. Our analysis widens the known ranges of nonlinearities for which classical positive solutions of semilinear elliptic systems are a priori bounded. Using these a priori bounds, and local and global bifurcation techniques, we prove the existence of positive solutions for a corresponding parametrized semilinear elliptic system. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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