Positive solutions for the Robin p-Laplacian problem with competing nonlinearities

By Leszek Gasinski, Nikolaos S. Papageorgiou. Advances in Calculus of Variations, 2019

56 citations recorded by the source corpus.

Abstract We consider a parametric nonlinear elliptic equation driven by the Robin p-Laplacian. The reaction term is a Carathéodory function which exhibits competing nonlinearities (concave and convex terms). We prove two bifurcation-type results describing the set of positive solutions as the parameter varies. In the process we also prove two strong comparison principles for Robin equations. These results are proved for differential operators which are more general than the p-Laplacian and need not be homogeneous.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/39805f19204ba989e638286dddcce38d6bc0fbe3

Citations in the corpus

• Existence and multiplicity of solutions for double‐phase Robin problems (2020, unknown): “N. S. Papageorgiou, C. Vetro and F. Vetro, ‘Multiple solutions for parametric double phase Dirichlet problems’, Commun.”