Minimax Theory and its Applications 01 (2016), No. 1, 083--109
Copyright Heldermann Verlag 2016
On Resonant (p,2)-Equations
DICEAM, Facoltà di Ingegneria, Università di Reggio Calabria, Via Graziella - Loc. Feo di Vito, 89122 Reggio Calabria, Italy
Dept. of Engineering and Applied Mathematics, University of Messina, 98166 Messina, Italy, Italy
Nikolaos S. Papageorgiou
Dept. of Mathematics, National Technical University, Zografou Campus, Athens 15780, Greece
We consider a nonlinear nonhomogeneous elliptic equation driven by the sum of a p-Laplacian and a Laplacian (p,2)-equation with a Carathéodory reaction which at ±∞ is resonant with respect to the principal eigenvalue of the negative Dirichlet p-Laplacian. Using minimax methods based on the critical point theory, together with truncation techniques and Morse theory, we obtain multiplicity results producing three or four solutions with sign information (constant sign solutions and nodal solutions).
Keywords: Minimax characterization, nonlinear regularity, nonlinear maximum principle, nodal solutions, resonant equation.
MSC: 35J20, 35J60; 58E05
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