|Title||PARAMETRIC p-LAPLACIAN EQUATIONS WITH SUPERLINEAR REACTIONS|
|Publication Type||Journal Article|
|Year of Publication||2015|
|Authors||GASINSKI LESZEK, PAPAGEORGIOU NIKOLAOS|
|Journal||Dynamic Systems and Applications|
|AMS Subject Classification||35J20, 35J60, 35J92, 58E05|
We consider a parametric nonlinear Dirichlet problem driven by the p-Laplacian and with a Carath´eodory reaction which is (p − 1)-superlinear near ±∞ (but without satisfying the Ambrosetti-Rabinowitz condition) and (p − 1)-sublinear near zero. We show that for all values of the parameter λ > 0, the problem has at least three nontrivial solutions (two of constant sign). If we alter the geometry near the origin by introducing a “concave” nonlinearity (problem with combined nonlinearities), we show the existence of at least five nontrivial solutions (four of constant sign and the fifth nodal), when the parameter λ > 0 is small. Also, we produce extremal constant sign solutions u∗λ ∈ -int C+ and v∗λ ∈ −int C+. We investigate the monotonicity and continuity properties of the map λ→ u∗λ .