Ground state sign-changing solutions for a class of quasilinear Schrödinger equations
In this paper, we consider the following quasilinear Schrödinger equation: −Δu+V(x)u+κ2Δ(u2)u=K(x)f(u),x∈RN,-\Delta u+V\left(x)u+\frac{\kappa }{2}\Delta \left({u}^{2})u=K\left(x)f\left(u),\hspace{1.0em}x\in {{\mathbb{R}}}^{N}, where N≥3N\ge 3, κ>0\kappa \gt 0, f∈C(R,R)f\in {\mathcal{C}}\left({\ma...
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| Format: | Article |
| Language: | English |
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De Gruyter
2021-12-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2021-0134 |
| _version_ | 1819001743264972800 |
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| author | Zhu Wenjie Chen Chunfang |
| author_facet | Zhu Wenjie Chen Chunfang |
| author_sort | Zhu Wenjie |
| collection | DOAJ |
| description | In this paper, we consider the following quasilinear Schrödinger equation: −Δu+V(x)u+κ2Δ(u2)u=K(x)f(u),x∈RN,-\Delta u+V\left(x)u+\frac{\kappa }{2}\Delta \left({u}^{2})u=K\left(x)f\left(u),\hspace{1.0em}x\in {{\mathbb{R}}}^{N}, where N≥3N\ge 3, κ>0\kappa \gt 0, f∈C(R,R)f\in {\mathcal{C}}\left({\mathbb{R}},{\mathbb{R}}), V(x)V\left(x) and K(x)K\left(x) are positive continuous potentials. Under given conditions, by changing variables and truncation argument, the energy of ground state solutions of the Nehari type is achieved. We also prove the existence of ground state sign-changing solutions for the aforementioned equation. Our results are the generalization work of M. B. Yang, C. A. Santos, and J. Z. Zhou, Least action nodal solution for a quasilinear defocusing Schrödinger equation with supercritical nonlinearity, Commun. Contemp. Math. 21 (2019), no. 5, 1850026, https://doi.org/10.1142/S0219199718500268. |
| first_indexed | 2024-12-20T22:54:04Z |
| format | Article |
| id | doaj.art-540822aaa10c4069b7fcef0c80701956 |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-20T22:54:04Z |
| publishDate | 2021-12-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-540822aaa10c4069b7fcef0c807019562022-12-21T19:24:09ZengDe GruyterOpen Mathematics2391-54552021-12-011911746175410.1515/math-2021-0134Ground state sign-changing solutions for a class of quasilinear Schrödinger equationsZhu Wenjie0Chen Chunfang1Department of Mathematics, Nanchang University, Nanchang, Jiangxi, 330031, P. R. ChinaDepartment of Mathematics, Nanchang University, Nanchang, Jiangxi, 330031, P. R. ChinaIn this paper, we consider the following quasilinear Schrödinger equation: −Δu+V(x)u+κ2Δ(u2)u=K(x)f(u),x∈RN,-\Delta u+V\left(x)u+\frac{\kappa }{2}\Delta \left({u}^{2})u=K\left(x)f\left(u),\hspace{1.0em}x\in {{\mathbb{R}}}^{N}, where N≥3N\ge 3, κ>0\kappa \gt 0, f∈C(R,R)f\in {\mathcal{C}}\left({\mathbb{R}},{\mathbb{R}}), V(x)V\left(x) and K(x)K\left(x) are positive continuous potentials. Under given conditions, by changing variables and truncation argument, the energy of ground state solutions of the Nehari type is achieved. We also prove the existence of ground state sign-changing solutions for the aforementioned equation. Our results are the generalization work of M. B. Yang, C. A. Santos, and J. Z. Zhou, Least action nodal solution for a quasilinear defocusing Schrödinger equation with supercritical nonlinearity, Commun. Contemp. Math. 21 (2019), no. 5, 1850026, https://doi.org/10.1142/S0219199718500268.https://doi.org/10.1515/math-2021-0134quasilinear schrödinger equationsground state sign-changing solutionschange of variablesl∞-estimate35j6035j20 |
| spellingShingle | Zhu Wenjie Chen Chunfang Ground state sign-changing solutions for a class of quasilinear Schrödinger equations Open Mathematics quasilinear schrödinger equations ground state sign-changing solutions change of variables l∞-estimate 35j60 35j20 |
| title | Ground state sign-changing solutions for a class of quasilinear Schrödinger equations |
| title_full | Ground state sign-changing solutions for a class of quasilinear Schrödinger equations |
| title_fullStr | Ground state sign-changing solutions for a class of quasilinear Schrödinger equations |
| title_full_unstemmed | Ground state sign-changing solutions for a class of quasilinear Schrödinger equations |
| title_short | Ground state sign-changing solutions for a class of quasilinear Schrödinger equations |
| title_sort | ground state sign changing solutions for a class of quasilinear schrodinger equations |
| topic | quasilinear schrödinger equations ground state sign-changing solutions change of variables l∞-estimate 35j60 35j20 |
| url | https://doi.org/10.1515/math-2021-0134 |
| work_keys_str_mv | AT zhuwenjie groundstatesignchangingsolutionsforaclassofquasilinearschrodingerequations AT chenchunfang groundstatesignchangingsolutionsforaclassofquasilinearschrodingerequations |