6533b860fe1ef96bd12c30c6
RESEARCH PRODUCT
(p, 2)-Equations with a Crossing Nonlinearity and Concave Terms
Calogero VetroNikolaos S. PapageorgiouFrancesca Vetrosubject
Dirichlet problem0209 industrial biotechnologyControl and OptimizationMultiple smooth solutionTruncationConcave termApplied Mathematicsp-Laplacian010102 general mathematicsMathematical analysis02 engineering and technology01 natural sciencesTerm (time)Nonlinear system020901 industrial engineering & automationSettore MAT/05 - Analisi MatematicaCrossing nonlinearityNonlinear maximum principle0101 mathematicsLaplace operatorCritical groupNonlinear regularityMorse theoryParametric statisticsMathematicsdescription
We consider a parametric Dirichlet problem driven by the sum of a p-Laplacian ($$p>2$$) and a Laplacian (a (p, 2)-equation). The reaction consists of an asymmetric $$(p-1)$$-linear term which is resonant as $$x \rightarrow - \infty $$, plus a concave term. However, in this case the concave term enters with a negative sign. Using variational tools together with suitable truncation techniques and Morse theory (critical groups), we show that when the parameter is small the problem has at least three nontrivial smooth solutions.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2018-02-14 | Applied Mathematics & Optimization |