TY - JOUR

T1 - Multiple solutions for nonlinear nonhomogeneous resonant coercive problems

AU - Tornatore, Elisabetta

AU - Averna, Diego

AU - Papageorgiou, Nikolaos S.

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

KW - Analysis

KW - Applied Mathematics

KW - Constant sign and nodal solutions

KW - Critical groups

KW - Discrete Mathematics and Combinatorics

KW - Extremal constant sign solutions

KW - Multiple smooth solutions

KW - Nonlinear regularity

KW - Resonance

KW - Analysis

KW - Applied Mathematics

KW - Constant sign and nodal solutions

KW - Critical groups

KW - Discrete Mathematics and Combinatorics

KW - Extremal constant sign solutions

KW - Multiple smooth solutions

KW - Nonlinear regularity

KW - Resonance

UR - http://hdl.handle.net/10447/265013

UR - http://aimsciences.org/journals/pdfs.jsp?paperID=14664&mode=full

M3 - Article

VL - 11

SP - 155

EP - 178

JO - DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S

JF - DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS. SERIES S

SN - 1937-1632

ER -