Positive solutions and multiple solutions for periodic problems driven by scalarp -Laplacian
In this paper we study a nonlinear second order periodic problem driven by a scalar p ‐Laplacian and with a nonsmooth, locally Lipschitz potential function. Using a variational approach based on the nonsmooth critical point theory for locally Lipschitz functions, we first prove the existence of nontrivial positive solutions and then establish the existence of a second distinct solution (multiplicity theorem) by strengthening further the hypotheses.
nonsmooth critical point theory, locally Lipschitz function, generalized subdifferential, nonsmooth PS ‐condition, Mountain Pass Theorem, positive solution, multiple solutions
Hu, Shouchuan, and Nikolaos S. Papageorgiou. "Positive solutions and multiple solutions for periodic problems driven by scalar p‐Laplacian." Mathematische Nachrichten 279, no. 12 (2006): 1321-1334.