Nonlinear nonhomogeneous periodic problems

作者：Barletta Giuseppina^*; D'Agui Giuseppina^*; Papageorgiou Nikolaos S^*

来源：Nodea-Nonlinear Differential Equations and Applications, 2016, 23(2): 18.

DOI：10.1007/s00030-016-0356-3

• Constant sign solutions
• Extremal solutions
• Nodal solutions
• Nonlinear maximum principle
• Critical groups

We consider a nonlinear periodic problem driven by a nonhomogeneous differential operator and a Caratheodory reaction. We show that it has at least three solutions, two of constant sign and the third nodal. In the particular case of the scalar p-Laplacian and with a parametric reaction of equidiffusive type, we show that three solutions with precise sign exist if the parameter lambda > (lambda(1)) over cap (p) = the first nonzero eigenvalue of the periodic scalar Laplacian. Finally, in the semilinear case p = 2), we show that there is a second nodal solution, for a total of four nontrivial solutions all with sign information.

• 出版日期2016-4