Three non-trivial solutions for not necessarily coercive p-Laplacian equations
We consider the existence of three non-trivial smooth solutions for nonlinear elliptic problems driven by the p-Laplacian. Using variational arguments, coupled with the method of upper and lower solutions, critical groups and suitable truncation techniques, we produce three non-trivial smooth solutions, two of which have constant sign. The hypotheses incorporate both coercive and non-coercive problems in our framework of analysis.
Critical groups, Non-trivial solutions, Nonlinear regularity, P-Laplacian, Truncations, Upper and lower solutions
Hu, Shouchuan, and Nikolas S. Papageorgiou. "Three non-trivial solutions for not necessarily coercive p-Laplacian equations." Proceedings of the Edinburgh Mathematical Society 52, no. 3 (2009): 679-688.
Proceedings of the Edinburgh Mathematical Society