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Ground State Solution of Pohožaev Type for Quasilinear Schrödinger Equation Involving Critical Exponent in Orlicz Space

Author

Listed:
  • Jianqing Chen

    (College of Mathematics and Informatics & FJKLMAA, Fujian Normal University, Fuzhou 350117, China
    These authors contributed equally to this work.)

  • Qian Zhang

    (College of Mathematics and Informatics & FJKLMAA, Fujian Normal University, Fuzhou 350117, China)

Abstract

We study the following quasilinear Schrödinger equation involving critical exponent − Δ u + V ( x ) u − Δ ( u 2 ) u = A ( x ) | u | p − 1 u + λ B ( x ) u 3 N + 2 N − 2 , u ( x ) > 0 for x ∈ R N and u ( x ) → 0 as | x | → ∞ . By using a monotonicity trick and global compactness lemma, we prove the existence of positive ground state solutions of Pohožaev type. The nonlinear term | u | p − 1 u for the well-studied case p ∈ [ 3 , 3 N + 2 N − 2 ) , and the less-studied case p ∈ [ 2 , 3 ) , and for the latter case few existence results are available in the literature. Our results generalize partial previous works.

Suggested Citation

  • Jianqing Chen & Qian Zhang, 2019. "Ground State Solution of Pohožaev Type for Quasilinear Schrödinger Equation Involving Critical Exponent in Orlicz Space," Mathematics, MDPI, vol. 7(9), pages 1-21, August.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:9:p:779-:d:260444
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