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摘要
We consider a nonlinear periodic problem driven by the scalar p-Laplacian and with a reaction term which exhibits a (p - 1)-superlinear growth near +/-infinity but need not satisfy the Ambrosetti-Rabinowitz condition. Combining critical point theory with Morse theory we prove an existence theorem. Then, using variational methods together with truncation techniques, we prove a multiplicity theorem establishing the existence of at least five non-trivial solutions, with precise sign information for all of them (two positive solutions, two negative solutions and a nodal (sign changing) solution).
- 出版日期2013-10
- 单位中国人民解放军海军大连舰艇学院
