We consider nonlinear periodic problems driven by the sum of a scalar p-Laplacian and a scalar Laplacian and a Caratheodory reaction, which at ±∞, is resonant with respect to any higher eigenvalue. Using variational methods, coupled with suitable perturbation and truncation techniques and Morse theory, we prove a three solutions theorem. For equations resonant with respect to the principal eigenvalue λ^0=0, we establish the existence of nodal solutions.
Nonlinear resonant periodic problems / Papageorgiou, N. S.; Papalini, Francesca. - In: DIFFERENTIAL AND INTEGRAL EQUATIONS. - ISSN 0893-4983. - STAMPA. - 27:11/12(2014), pp. 1107-1146.
Nonlinear resonant periodic problems
PAPALINI, Francesca
2014-01-01
Abstract
We consider nonlinear periodic problems driven by the sum of a scalar p-Laplacian and a scalar Laplacian and a Caratheodory reaction, which at ±∞, is resonant with respect to any higher eigenvalue. Using variational methods, coupled with suitable perturbation and truncation techniques and Morse theory, we prove a three solutions theorem. For equations resonant with respect to the principal eigenvalue λ^0=0, we establish the existence of nodal solutions.File in questo prodotto:
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