The aim of this paper is to investigate the existence of solutions of the semilinear elliptic problem {−Δu = p(x,u)+εg(x,u) inΩ, u=0 on∂Ω where Ω is an open bounded domain of RN, ε∈R,p is subcritical and asymptotically linear at infinity, and g is just a continuous function. Even when this problem has not a variational structure on H10(Ω), suitable procedures and estimates allow us to prove that the number of distinct critical levels of the functional associated to the unperturbed problem is “stable” under small perturbations, in particular obtaining multiplicity results if p is odd, both in the non-resonant and in the resonant case.
Perturbed asymptotically linear problems / Bartolo, Rossella; Candela, A. M.; Salvatore, A.. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 193:1(2014), pp. 89-101. [10.1007/s10231-012-0267-9]
Perturbed asymptotically linear problems
BARTOLO, Rossella;
2014-01-01
Abstract
The aim of this paper is to investigate the existence of solutions of the semilinear elliptic problem {−Δu = p(x,u)+εg(x,u) inΩ, u=0 on∂Ω where Ω is an open bounded domain of RN, ε∈R,p is subcritical and asymptotically linear at infinity, and g is just a continuous function. Even when this problem has not a variational structure on H10(Ω), suitable procedures and estimates allow us to prove that the number of distinct critical levels of the functional associated to the unperturbed problem is “stable” under small perturbations, in particular obtaining multiplicity results if p is odd, both in the non-resonant and in the resonant case.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
