Multiple solutions for superlinear Dirichlet problems with an indefinite potential

作者：Kyritsi Sophia Th^*; Papageorgiou Nikolaos S

来源：Annali di Matematica Pura ed Applicata, 2013, 192(2): 297-315.

DOI：10.1007/s10231-011-0224-z

• Superlinear reaction
• Critical groups
• Mountainpass type critical point
• C-condition
• Morse relation
• Three solutions
• Indefinite potential

We consider a semilinear elliptic equation with an indefinite unbounded potential and a Carath,odory reaction term that exhibits superlinear growth near +/- a without satisfying the AR-condition. Also, at the origin, the primitive of the reaction satisfies a nonuniform nonresonance condition with respect to the first eigenvalue of . Using critical point theory and Morse theory, we show that the problem has at least three nontrivial smooth solutions. Our result extends that of Wang (Anal Nonlineaire 8:43-58, 1991).

• 出版日期2013-4
• 单位中国人民解放军海军大连舰艇学院