Document Type


Publication Date


Published In

Journal Of Mathematical Analysis And Applications


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.


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

Available for download on Wednesday, May 15, 2019

Included in

Mathematics Commons