Semilinear Robin Problems with Indefinite Potential and Competition Phenomena
We consider semilinear parametric Robin problems driven by the Laplacian plus an indefinite and unbounded potential. In the reaction we have two competing nonlinearities. However, the competition is different from the usual one in “concave-convex” problems. Using a combination of different tools we prove a multiplicity theorem producing seven nontrivial smooth solutions all with sign information (four of constant sign and three nodal).
Competition phenomena, Constant sign solutions, Critical groups, Flow invariance, Hopf boundary point theorem, Nodal solutions
Hu, Shouchuan, and Nikolaos S. Papageorgiou. "Semilinear Robin problems with indefinite potential and competition phenomena." Acta Applicandae Mathematicae 168, no. 1 (2020): 187-216.
Acta Applicandae Mathematicae