We consider a nonlinear, nonhomogeneous Dirichlet problem driven by the sum of a p-Laplacian (2 < p) and a Laplacian. The reaction term is a Caratheodory function f(z, x) which is resonant with respect to the principal eigenvalue of (- ∆_p, W_0^{1,p}(Ω)). Using variational methods combined with truncation and comparison techniques and Morse theory (critical groups) we prove the existence of three nontrivial smooth solutions all with sign information and under three different conditions concerning the behavior of f(z, ·) near zero. By strengthening the regularity of f(z, ·), we are able to generate a second nodal solution for a total of four nontrivial smooth solutions.

Averna, D., Papageorgiou, N., & Tornatore, E. (2018). Multiple solutions for nonlinear nonhomogeneous resonant coercive problems. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S, 11(2), 155-178 [10.3934/dcdss.2018010].

Multiple solutions for nonlinear nonhomogeneous resonant coercive problems

Averna, Diego;Tornatore, Elisabetta
2018

Abstract

We consider a nonlinear, nonhomogeneous Dirichlet problem driven by the sum of a p-Laplacian (2 < p) and a Laplacian. The reaction term is a Caratheodory function f(z, x) which is resonant with respect to the principal eigenvalue of (- ∆_p, W_0^{1,p}(Ω)). Using variational methods combined with truncation and comparison techniques and Morse theory (critical groups) we prove the existence of three nontrivial smooth solutions all with sign information and under three different conditions concerning the behavior of f(z, ·) near zero. By strengthening the regularity of f(z, ·), we are able to generate a second nodal solution for a total of four nontrivial smooth solutions.
http://aimsciences.org/journals/pdfs.jsp?paperID=14664&mode=full
Averna, D., Papageorgiou, N., & Tornatore, E. (2018). Multiple solutions for nonlinear nonhomogeneous resonant coercive problems. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S, 11(2), 155-178 [10.3934/dcdss.2018010].
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/265013
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