Infinitely many solutions for symmetric and non-symmetric elliptic systems

Abstract

We study an elliptic system equivalent to a fourth order elliptic equation. By using\ud variational and perturbative methods, we prove the existence of infinitely many solutions\ud both in the symmetric and in the non-symmetric case

Existence and multiplicity results for some Lane–Emden elliptic systems: Subquadratic case

“…However, as concerns the results of multiplicity, in literature there is a substantial difference between the subquadratic and the superquadratic case: indeed, di erent authors have found multiple solutions in the rst case (see [2,17,18]) while, to our knowledge, no multiplicity results have been proved in the second case.…”

Existence and multiplicity of solutions for a class of superlinear elliptic systems

“…Especially, de Figueiredo and Ruf [17] proved the existence of nontrivial solutions for system (1.1), where the function f is superlinear and with no growth restriction. By using variational and perturbative methods, Salvatore [29] established the existence of infinitely many solutions both in the symmetric and in the non-symmetric cases. The following result is stated in [29].…”

“…By using variational and perturbative methods, Salvatore [29] established the existence of infinitely many solutions both in the symmetric and in the non-symmetric cases. The following result is stated in [29]. Here, condition (f1) is the classical Ambrosetti-Rabinowitz condition, which was first used in [2].…”

“…In this paper, motivated by the works [9,17,27,29], we consider the existence and multiplicity of solutions for problem (1.1). We state our main results in the following theorems.…”

“…We state our main results in the following theorems. [9,29]. For example, F(s) = |s| q ln( + |s| q ) + sin |s| q − ln( + |s| q ) for all s ∈ ℝ.…”