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Existence of positive solutions for a system of quasilinear SchrΓΆdinger equation
  • Ayesha Baig,
  • Zhouxin Li
Ayesha Baig
Department of Mathematics and Statistics, Central South University

Corresponding Author:[email protected]

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Zhouxin Li
Department of Mathematics and Statistics, Central South University

Abstract

In this article, we investigate the presence of standing wave solutions for the given quasilinear SchrΓΆdinger system. { βˆ’πœ€ 2 Δ𝑒 + π‘Š(π‘₯)𝑒 βˆ’ πœ…πœ€ 2 Ξ”(𝑒 2)𝑒 = 𝑄 𝑒 (𝑒, 𝑣) 𝑖𝑛 ℝ 𝑁 βˆ’πœ€ 2 Δ𝑣 + 𝑉(π‘₯)𝑣 βˆ’ πœ…πœ€ 2 Ξ”(𝑣 2)𝑣 = 𝑄 𝑣 (𝑒, 𝑣) 𝑖𝑛 ℝ 𝑁 𝑒, 𝑣 > 0 in ℝ 𝑁 , 𝑒, 𝑣 ∈ 𝐻 1 (ℝ 𝑁).