MULTIPLE SOLUTIONS FOR A CLASS OF QUASILINEAR SCHRÖDINGER SYSTEM IN ℝ^N

Abstract

Abstract. This paper is concerned with the quasilinear Schrödinger systemwhere N ≥ 3. The potential functions a(x), b(x) ∈ L ∞ (R N ) are bounded in R N . By using mountain pass theorem and the Ekeland variational principle, we prove that there are at least two solutions to system (0.1).

Quasilinear Schrödinger Systems Involving Critical Exponential Growth

“…In the literature, there are recent mathematical studies on the existence of solutions for systems of the form (1.1) when the dimension N ≥ 3, we can cite for instance [4,5,6,7,16]. However, as far as we know, our work is the first that leads with quasilinear systems involving critical growth exponential in the sense of Trudinger-Moser inequality.…”