Positive Periodic and Homoclinic Solutions for Nonlinear Differential Equations with Nonsmooth Potential
We study the existence of positive solutions and of positive homoclinic (to zero) solutions for a class of periodic problems driven by the scalar ordinary p-Laplacian and having a nonsmooth potential. Our approach is variational based on the nonsmooth critical point theory and our results extend the recent works of Korman–Lazer (Electronic JDE (1994)) and of Grossinho–Minhos–Tersian (J. Math. Anal. Appl. 240 (1999)).
Hu, Shouchuan, and Nikolaos S. Papageorgiou. "Positive periodic and homoclinic solutions for nonlinear differential equations with nonsmooth potential." Positivity 10, no. 2 (2006): 343-363.