Year: 2019
Type: article
Abstract: The aim of this paper is to investigate the existence of one or more critical points of a family of functionals which generalizes the model problem [Formula: see text] in the Banach space [Formula: see text], where [Formula: see text] is an open bounded domain, [Formula: see text] and the real terms [Formula: see text] and [Formula: see text] are [Formula: see text] Carathéodory functions on [Formula: see text]. We prove that, even if the coefficient [Formula: see text] makes the variational approach more difficult, if it satisfies “good” growth assumptions then at least one critical point exists also when the nonlinear term [Formula: see text] has a suitable supercritical growth. Moreover, if the functional is even, it has infinitely many critical levels. The proof, which exploits the interaction between two different norms on [Formula: see text], is based on a weak version of the Cerami–Palais–Smale condition and a suitable intersection lemma which allow us to use a Mountain Pass Theorem.
Authors: A. M. Candela, G. Palmieri, A. Salvatore
Institution: University of Bari Aldo Moro
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2989115695