We consider a nonlinear periodic problem driven by a nonhomogeneous differential operator and a Carath´eodory 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 λ >λ_1(p)= the first nonzero eigenvalue ofthe periodic scalar Laplacian. Finally, in the semilinear case (p = 2), weshow that there is a second nodal solution, for a total of four nontrivial solutions all with sign information.

Nonlinear nonhomogeneous periodic problems

BARLETTA, Giuseppina
;
2016

Abstract

We consider a nonlinear periodic problem driven by a nonhomogeneous differential operator and a Carath´eodory 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 λ >λ_1(p)= the first nonzero eigenvalue ofthe periodic scalar Laplacian. Finally, in the semilinear case (p = 2), weshow that there is a second nodal solution, for a total of four nontrivial solutions all with sign information.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.12318/2004
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