0000000000670890

AUTHOR

N. S. Papageorgiou

showing 2 related works from this author

Positive solutions for nonlinear Robin problems

2017

We consider a parametric Robin problem driven by the p-Laplacian with an indefinite potential and with a superlinear reaction term which does not satisfy the Ambrosetti-Rabinowitz condition. We look for positive solutions. We prove a bifurcation-type theorem describing the nonexistence, existence and multiplicity of positive solutions as the parameter varies. We also show the existence of a minimal positive solution $\tilde{u}_\lambda$ and establish the monotonicity and continuity of the map $\lambda\to \tilde{u}_\lambda$.

truncation and comparison techniquesminimax positive solutionSettore MAT/05 - Analisi Matematicalcsh:MathematicsMathematics::Analysis of PDEssuperlinear reactionRobin boundary condition superlinear reaction truncation and comparison techniques bifurcation-type result minimax positive solutionRobin boundary conditionbifurcation-type resultlcsh:QA1-939
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Bifurcation phenomena for the positive solutions of semilinear elliptic problems with mixed boundary conditions

2016

We consider a parametric semilinear elliptic equation with a Cara-theodory reaction which exhibits competing nonlinearities. It is "concave" (sub-linear) near the origin and "convex" (superlinear) or linear near $+\infty$. Using variational methods based on the critical point theory, coupled with suitable truncation and comparison techniques, we prove a bifurcation-type theorem, describing the set of positive solutions as the parameter varies.

Positive solutionTruncationCerami conditionMixed boundary conditionMountain pass theoremBifurcation-type theorem
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