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Existence and Concentration of Positive Ground State Solutions for a (p, Q)-kirchhoff Type Equation With Moser-trudinger Nonlinearity

Year: 2026
Type: article
Abstract: In this work, we concern the existence and concentration of positive ground state solutions for the following $ (p, q) $-Kirchhoff type problem $ \left\{\begin{array}{ll} \quad-(1+a\int_{\mathbb{R}^N}|\nabla u|^pdx)\Delta_p u-(1+b\int_{\mathbb{R}^N}|\nabla u|^qdx)\Delta_q u+V(\varepsilon x)(|u|^{p-2}u+|u|^{q-2}u)\ \\ =f(u) \quad \text{in}\, \mathbb{R}^N, \, u\in W^{1, p}(\mathbb{R}^N)\cap W^{1, q}(\mathbb{R}^N), \quad u>0 \, \, \text{in}\, \, \mathbb{R}^N, \end{array}\right. $ where $ \varepsilon>0 $ is a small parameter, $ a, b>0, 1 m-Laplacian operator, the potential $ V: \mathbb{R}^N\rightarrow \mathbb{R} $ is a positive continuous function and $ f: \mathbb{R}\rightarrow \mathbb{R} $ is a continuous nonlinearity involving critical exponential growth and not satisfying usual Ambrosetti-Rabinowitz condition. The existence and concentration behavior of positive ground state solutions are established by variational methods combined with some sharp exponential type inequalities.
Language: English
Open Access status: diamond
OpenAlex ID: W7133329706
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Cites: 28
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