6533b831fe1ef96bd129991d
RESEARCH PRODUCT
Nonlinear nonhomogeneous Neumann eigenvalue problems
Roberto LivreaPasquale CanditoNikolaos S. Papageorgiousubject
Applied MathematicsConcave termnodal solutionMathematical analysisZero (complex analysis)superlinear reactionDifferential operatorExtremal constant sign solutionNonlinear systemMaximum principlemaximum principleNeumann boundary conditionextremal constant sign solutionsQA1-939superlinear reaction concave terms maximum principle extremal constant sign solutions nodal solution critical groupsconcave termsConstant (mathematics)critical groupsEigenvalues and eigenvectorsCritical groupMathematicsMathematicsSign (mathematics)description
We consider a nonlinear parametric Neumann problem driven by a nonhomogeneous differential operator with a reaction which is $(p-1)$-superlinear near $\pm\infty$ and exhibits concave terms near zero. We show that for all small values of the parameter, the problem has at least five solutions, four of constant sign and the fifth nodal. We also show the existence of extremal constant sign solutions.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2015-07-01 | Electronic Journal of Qualitative Theory of Differential Equations |