We look for standing waves of nonlinear Schrödinger equationcoupled with Maxwell’s equations. We use the variational formulation introduced by Benci and Fortunato in 1992 for studying an eigenvalue problem for the Schrödinger-Maxwell system in bounded domains. We establish the existence of multiple standing waves both in the homogeneous and the non-homogeneous cases by means of the fibering method introduced by Pohozaev.
We prove the existence of infinitely many solutions for symmetric elliptic systems with nonlinearities of\ud
arbitrary growth. Moreover, if the symmetry of the problem is broken by a small enough perturbation term,\ud
we find at least three solutions. The proofs utilise a variational setting given by de Figueiredo and Ruf in\ud
order to prove an existence’s result and the “algebraic” approach based on the Pohozaev’s fibering method
Abstract. The aim of this paper is investigating the existence and the multiplicity of weak solutions of the quasilinear elliptic problemwith smooth boundary ∂Ω and the nonlinearity g behaves as u p−1 at infinity. The main tools of the proof are some abstract critical point theorems in Bartolo et al. (Nonlinear Anal. 7: 981-1012, 1983, but extended to Banach spaces, and two sequences of quasi-eigenvalues for the p-Laplacian operator as in Candela and Palmieri (Calc.
The aim of this paper is investigating the existence of one or more critical points of a family of functionals which generalizes the model problemis an open bounded domain, 1 < p < N and the real termsĀ(x, t) and G(x, t) are C 1 Carathéodory functions on Ω × R.We prove that, even if the coefficientĀ(x, t) makes the variational approach more difficult, if it satisfies "good" growth assumptions then at least one critical point exists also when the nonlinear term G(x, t) 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 X, 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.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.