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

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.

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