Ground states to a quasilinear Schrödinger equation with Berestycki-Lions type nonlinearities
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918115015655424 |
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| author | Yang, Xianyong Jia, Yue |
| author_facet | Yang, Xianyong Jia, Yue |
| contents | In this paper, we study the following quasilinear {S}chrödinger equation: $$\left\{ \begin{array}{l} - {Δu} - \frac{κ}{2}Δ\left( {u}^{2}\right) u = h\left( u\right) \text{ in }{\mathbb{R}}^{N}, \\ u \in {H}^{1}\left( {\mathbb{R}}^{N}\right), \end{array}\right. $$ where $N \geq 3,κ> 0$ is a parameter, and $h$ satisfies Berestycki-Lions condition. By using a critical point theory on a topological manifold, we obtain the existence of a ground state for $N \geq 3$, a nonradial ground state for $N \geq 4$, and infinitely many nonradial solutions for $N = 4$ or $N \geq 6$. Our results generalize several classical works into quasilinear equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_02141 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Ground states to a quasilinear Schrödinger equation with Berestycki-Lions type nonlinearities Yang, Xianyong Jia, Yue Analysis of PDEs In this paper, we study the following quasilinear {S}chrödinger equation: $$\left\{ \begin{array}{l} - {Δu} - \frac{κ}{2}Δ\left( {u}^{2}\right) u = h\left( u\right) \text{ in }{\mathbb{R}}^{N}, \\ u \in {H}^{1}\left( {\mathbb{R}}^{N}\right), \end{array}\right. $$ where $N \geq 3,κ> 0$ is a parameter, and $h$ satisfies Berestycki-Lions condition. By using a critical point theory on a topological manifold, we obtain the existence of a ground state for $N \geq 3$, a nonradial ground state for $N \geq 4$, and infinitely many nonradial solutions for $N = 4$ or $N \geq 6$. Our results generalize several classical works into quasilinear equations. |
| title | Ground states to a quasilinear Schrödinger equation with Berestycki-Lions type nonlinearities |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2505.02141 |