6533b851fe1ef96bd12a8f15

RESEARCH PRODUCT

Solutions and positive solutions for superlinear Robin problems

Francesca VetroCalogero VetroNikolaos S. Papageorgiou

subject

Pure mathematicsnonlinear maximum principle010102 general mathematicsMathematics::Analysis of PDEssuperlinear reactionStatistical and Nonlinear PhysicsMultiplicity (mathematics)01 natural sciencesTerm (time)Nonlinear systempositive solutionSettore MAT/05 - Analisi Matematica0103 physical sciencesNonhomogeneous differential operatornonlinear regularity010307 mathematical physics0101 mathematicscritical groupsMathematical PhysicsMathematics

description

We consider nonlinear, nonhomogeneous Robin problems with a (p − 1)-superlinear reaction term, which need not satisfy the Ambrosetti-Rabinowitz condition. We look for positive solutions and prove existence and multiplicity theorems. For the particular case of the p-Laplacian, we prove existence results under a different geometry near the origin.We consider nonlinear, nonhomogeneous Robin problems with a (p − 1)-superlinear reaction term, which need not satisfy the Ambrosetti-Rabinowitz condition. We look for positive solutions and prove existence and multiplicity theorems. For the particular case of the p-Laplacian, we prove existence results under a different geometry near the origin.

https://doi.org/10.1063/1.5118760