Title

A Priori Bounds And Existence Of Positive Solutions For Semilinear Elliptic Systems

Document Type

Article

Publication Date

5-15-2017

Published In

Journal Of Mathematical Analysis And Applications

Abstract

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.

Keywords

A priori estimates, Semilinear elliptic systems, Critical Sobolev hyperbola, Moving planes method, Rellich–Pohozaev identity, Biparameter bifurcation

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