Abstract
We consider the following quasilinear Schrödinger equation involving p-Laplacian
where \(N > p > 1,\,\,\eta \ge {p \over {2(p - 1)}},\,\,p < q < 2\eta {p^ * }(\mu ),\,\,{p^ * }(s) = {{p(N - s)} \over {N - p}}\), and λ, μ, ν are parameters with λ > 0, μ, ν ∈ [0, p). Via the Mountain Pass Theorem and the Concentration Compactness Principle, we establish the existence of nontrivial ground state solutions for the above problem.
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Wang is supported by the National Natural Science Foundation of China (12226411) and the Research Ability Cultivation Fund of HUAS (No.2020kypytd006). Gao is supported by the National Natural Science Foundation of China (11931012, 11871386) and the Fundamental Research Funds for the Central Universities (WUT: 2020IB019).
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Wang, Jx., Gao, Q. On the Existence of Ground State Solutions to a Quasilinear Schrödinger Equation involving p-Laplacian. Acta Math. Appl. Sin. Engl. Ser. 39, 381–395 (2023). https://doi.org/10.1007/s10255-023-1053-8
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DOI: https://doi.org/10.1007/s10255-023-1053-8