MULTIPLICITY OF SOLUTIONS FOR RESONANT NEUMANN PROBLEMS WITH AN INDEFINITE AND UNBOUNDED POTENTIAL

作者：Papageorgiou Nikolaos S^*; Radulescu Vicentiu D

来源：Transactions of the American Mathematical Society, 2015, 367(12): 8723-8756.

• Indefinite and unbounded potential
• reduction method
• resonance
• unique continuation property
• regularity
• critical groups

We examine semilinear Neumann problems driven by the Laplacian plus an unbounded and indefinite potential. The reaction is a Caratheodory function which exhibits linear growth near +/-infinity. We allow for resonance to occur with respect to a nonprincipal nonnegative eigenvalue, and we prove several multiplicity results. Our approach uses critical point theory, Morse theory and the reduction method (the Lyapunov-Schmidt method).

• 出版日期2015-12