On a new class of elliptic systems with nonlinearities of arbitrary growth

Abstract

We guarantee the existence of infinitely many different pairs of solutions to the systemΩ is a bounded domain in R N and the continuous nonlinear term f has an unusual oscillatory behavior. The sequence of solutions tends to zero (resp., infinity) with respect to certain norms and the nonlinear term f may enjoy an arbitrary growth at infinity (resp., at zero) whenever f oscillates near zero (resp., at infinity). Our results provide the first applications of Ricceri's variational principle in the theory of coupled elliptic systems.

Infinitely many solutions for resonance elliptic systems

“…Furthermore, compared with their proofs, ours are much simpler. For more general operator, we refer the reader to the papers [3,4,9]. We cite the very recent monograph by Kristály, Rȃdulescu and Varga [10] as a general reference for the basic notions used in the paper.…”