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arXiv · 1406.5275

Maximal existence domains of positive solutions for two-parametric systems of elliptic equations

Vladimir Bobkov·Yavdat Il'yasov
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Abstract

The paper is devoted to the study of two-parametric families of Dirichlet problems for systems of equations with $p, q$-Laplacians and indefinite nonlinearities. Continuous and monotone curves $Γ_f$ and $Γ_e$ on the parametric plane $λ\times μ$, which are the lower and upper bounds for a maximal domain of existence of weak positive solutions are introduced. The curve $Γ_f$ is obtained by developing our previous work \cite{BobkovIlyasov} and it determines a maximal domain of the applicability of the Nehari manifold and fibering methods. The curve $Γ_e$ is derived explicitly via minimax variational principle of the extended functional method.

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Vladimir Bobkov, Yavdat Il'yasov. 2015-04-22. Maximal existence domains of positive solutions for two-parametric systems of elliptic equations. https://doi.org/10.1080/17476933.2015.1107905

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