On a class of superlinear nonlocal fractional problems without Ambrosetti–Rabinowitz type conditions
In this note, we deal with the existence of infinitely many solutions for a problem driven by nonlocal integro-differential operators with homogeneous Dirichlet boundary conditions \begin{equation*} \begin{cases} -\mathcal{L}_{K}u=\lambda f(x,u), & {\rm in}\ \Omega, \\ u=0, &{\rm i...
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| Format: | Article |
| Language: | English |
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University of Szeged
2019-03-01
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| Series: | Electronic Journal of Qualitative Theory of Differential Equations |
| Subjects: | |
| Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=7269 |
| _version_ | 1827951124348403712 |
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| author | Qing-Mei Zhou |
| author_facet | Qing-Mei Zhou |
| author_sort | Qing-Mei Zhou |
| collection | DOAJ |
| description | In this note, we deal with the existence of infinitely many solutions for a problem driven by nonlocal integro-differential operators with homogeneous Dirichlet boundary conditions
\begin{equation*}
\begin{cases}
-\mathcal{L}_{K}u=\lambda f(x,u), & {\rm in}\ \Omega, \\
u=0, &{\rm in}\;\mathbb{R}^{n}\backslash\Omega, \\
\end{cases}
\end{equation*}
where $\Omega$ is a smooth bounded domain of $\mathbb{R}^{n}$ and the nonlinear term $f$ satisfies superlinear at infinity but does not satisfy the the Ambrosetti–Rabinowitz type condition. The aim is to determine the precise positive interval of $\lambda$ for which the problem admits at least two nontrivial solutions by using abstract critical point results for an energy functional satisfying the Cerami condition. |
| first_indexed | 2024-04-09T13:36:53Z |
| format | Article |
| id | doaj.art-0f1133ed1ce44d96a83f569775fa1b01 |
| institution | Directory Open Access Journal |
| issn | 1417-3875 |
| language | English |
| last_indexed | 2024-04-09T13:36:53Z |
| publishDate | 2019-03-01 |
| publisher | University of Szeged |
| record_format | Article |
| series | Electronic Journal of Qualitative Theory of Differential Equations |
| spelling | doaj.art-0f1133ed1ce44d96a83f569775fa1b012023-05-09T07:53:09ZengUniversity of SzegedElectronic Journal of Qualitative Theory of Differential Equations1417-38752019-03-0120191711210.14232/ejqtde.2019.1.177269On a class of superlinear nonlocal fractional problems without Ambrosetti–Rabinowitz type conditionsQing-Mei Zhou0Northeast Forestry University, Harbin, P.R. ChinaIn this note, we deal with the existence of infinitely many solutions for a problem driven by nonlocal integro-differential operators with homogeneous Dirichlet boundary conditions \begin{equation*} \begin{cases} -\mathcal{L}_{K}u=\lambda f(x,u), & {\rm in}\ \Omega, \\ u=0, &{\rm in}\;\mathbb{R}^{n}\backslash\Omega, \\ \end{cases} \end{equation*} where $\Omega$ is a smooth bounded domain of $\mathbb{R}^{n}$ and the nonlinear term $f$ satisfies superlinear at infinity but does not satisfy the the Ambrosetti–Rabinowitz type condition. The aim is to determine the precise positive interval of $\lambda$ for which the problem admits at least two nontrivial solutions by using abstract critical point results for an energy functional satisfying the Cerami condition.http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=7269integrodifferential operatorsvariational methodweak solutionssign-changing potential |
| spellingShingle | Qing-Mei Zhou On a class of superlinear nonlocal fractional problems without Ambrosetti–Rabinowitz type conditions Electronic Journal of Qualitative Theory of Differential Equations integrodifferential operators variational method weak solutions sign-changing potential |
| title | On a class of superlinear nonlocal fractional problems without Ambrosetti–Rabinowitz type conditions |
| title_full | On a class of superlinear nonlocal fractional problems without Ambrosetti–Rabinowitz type conditions |
| title_fullStr | On a class of superlinear nonlocal fractional problems without Ambrosetti–Rabinowitz type conditions |
| title_full_unstemmed | On a class of superlinear nonlocal fractional problems without Ambrosetti–Rabinowitz type conditions |
| title_short | On a class of superlinear nonlocal fractional problems without Ambrosetti–Rabinowitz type conditions |
| title_sort | on a class of superlinear nonlocal fractional problems without ambrosetti rabinowitz type conditions |
| topic | integrodifferential operators variational method weak solutions sign-changing potential |
| url | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=7269 |
| work_keys_str_mv | AT qingmeizhou onaclassofsuperlinearnonlocalfractionalproblemswithoutambrosettirabinowitztypeconditions |