Nonlinear Neumann equations driven by a nonhomogeneous differential operator
We consider a nonlinear Neumann problem driven by a nonhomogeneous nonlinear differential operator and with a reaction which is (p-1)-superlinear without necessarily satisfying the Ambrosetti-Rabinowitz condition. A particular case of our differential operator is the p-Laplacian. By combining variational methods based on critical point theory with truncation techniques and Morse theory, we show that the problem has at least three nontrivial smooth solutions, two of which have constant sign (one positive and the other negative).
nonlinear regularity, morse relation, moser iteration method., Mountain Pass theorem, critical group, C-condition
Hu, Shouchuan, and Nikolaos S. Papageorgiou. "Nonlinear Neumann equations driven by a nonhomogeneous differential operator." Communications on Pure & Applied Analysis 10, no. 4 (2011): 1055.
Communications on Pure & Applied Analysis