Multiple existence results of solutions for quasilinear elliptic equations with a nonlinearity depending on a parameter

Dumitru Motreanu (1) , Mieko Tanaka (2)

1 LAMPS - LAboratoire de Modélisation Pluridisciplinaire et Simulations
2 Departement of Mathematics

We provide existence results of multiple solutions for quasilinear elliptic equations depending on a parameter under the Neumann and Dirichlet boundary condition. Our main result shows the existence of two opposite constant sign solutions and a sign changing solution in the case where we do not impose the subcritical growth condition to the nonlinear term not including derivatives of the solution. The studied equations contain the p-Laplacian problems as a special case. Our approach is based on variational methods combining superand sub-solution and the existence of critical points via descending flow.

Mots clés: Quasilinear elliptic equations; Nonhomogeneous operator; Super-solution and sub-solution; Critical point; Invariant sets of descending flow

Domaines: Mathématiques [math]

Dumitru Motreanu, Mieko Tanaka. Multiple existence results of solutions for quasilinear elliptic equations with a nonlinearity depending on a parameter. Annali di Matematica Pura ed Applicata, 2014, 193 (5), pp.1255-1282. ⟨10.1007/s10231-013-0327-9⟩. ⟨hal-01142979⟩