| Citation: |
Ruichang Pei, Hongming Xia. EXISTENCE AND CONCENTRATION OF POSITIVE GROUND STATE SOLUTIONS FOR A (P, Q)-KIRCHHOFF TYPE EQUATION WITH MOSER-TRUDINGER NONLINEARITY[J]. Journal of Applied Analysis & Computation, 2026, 16(4): 1784-1804. doi: 10.11948/20250228
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EXISTENCE AND CONCENTRATION OF POSITIVE GROUND STATE SOLUTIONS FOR A (P, Q)-KIRCHHOFF TYPE EQUATION WITH MOSER-TRUDINGER NONLINEARITY
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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<p<q=N, $ $ \Delta_m u=\mathrm{div}(|\nabla u|^{m-2}\nabla u) $ with $ m\in \{p, q\} $ is the 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.
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References
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Ruichang Pei, Hongming Xia. EXISTENCE AND CONCENTRATION OF POSITIVE GROUND STATE SOLUTIONS FOR A (P, Q)-KIRCHHOFF TYPE EQUATION WITH MOSER-TRUDINGER NONLINEARITY[J]. Journal of Applied Analysis & Computation, 2026, 16(4): 1784-1804. doi: 10.11948/20250228
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