RADIALLY SYMMETRIC SOLUTIONS FOR QUASILINEAR ELLIPTIC EQUATIONS INVOLVING NONHOMOGENEOUS OPERATORS IN AN ORLICZ-SOBOLEV SPACE SETTING

• 作者: Jae-Myoung KIM Yun-Ho KIM Jongrak LEE
• 来源期刊: 数学物理学报（英文版）
• 年，卷（期）: 2020,（6）
• 页码范围: 1679-1699
• 页数: 21页
• 语种: 英文

摘要

We investigate the following elliptic equations:{-M(∫RN φ(|▽u|2)dx)div(φ'(|▽u|2)▽u) +|ul|α-2u = λh(x,u),u(x) → 0, as |x| → ∞,in RN,where N ≥ 2, 1 ＜ p ＜ q ＜ N, α ＜ q, 1 ＜ α ≤ p*q'/p' with p* =Np/N-p,φ(t) behaves like tq/2 for small t and tp/2 for large t, and p' and q' are the conjugate exponents of p and q, respectively. We study the existence of nontrivial radially symmetric solutions for the problem above by applying the mountain pass theorem and the fountain theorem. Moreover,taking into account the dual fountain theorem, we show that the problem admits a sequence of small-energy, radially symmetric solutions.