We prove multiplicity of solutions for perturbed problems involving the square root of the Laplacian A = (-Delta)(1/2). More precisely, we consider the problem { Au = lambda u + f(x,u) + epsilon g(x,u) in Omega u = 0 on partial derivative Omega, where Omega subset of R-N is a bounded domain, epsilon is an element of R, N > 1, f is a subcritical function with asymptotic linear behavior at infinity, and g is a continuous function. We also show the invariance under small perturbations of the number of distinct critical levels of the associated energy functional to the unperturbed problem, in both resonant and non-resonant case.
Perturbed problems involving the square root of the Laplacian / Bartolo, Rossella; Colorado, Eduardo; Molica Bisci, Giovanni. - In: MINIMAX THEORY AND ITS APPLICATIONS. - ISSN 2199-1413. - STAMPA. - 4:1(2019), pp. 33-54.
Perturbed problems involving the square root of the Laplacian
Rossella Bartolo;
2019-01-01
Abstract
We prove multiplicity of solutions for perturbed problems involving the square root of the Laplacian A = (-Delta)(1/2). More precisely, we consider the problem { Au = lambda u + f(x,u) + epsilon g(x,u) in Omega u = 0 on partial derivative Omega, where Omega subset of R-N is a bounded domain, epsilon is an element of R, N > 1, f is a subcritical function with asymptotic linear behavior at infinity, and g is a continuous function. We also show the invariance under small perturbations of the number of distinct critical levels of the associated energy functional to the unperturbed problem, in both resonant and non-resonant case.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
