Existence and multiplicity for a superlinear elliptic problem under a non-quadradicity condition at infinity
In this article, we study the existence and multiplicity of solutions of the boundary-value problem $$\displaylines{ -\Delta u = f(x,u), \quad \text{in } \Omega, \cr u = 0, \quad \text{on } \partial\Omega, }$$ where $\Delta$ denotes the N-dimensional Laplacian, $\Omega$ is a bounded domain wi...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2020-06-01
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| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2020/60/abstr.html |
| _version_ | 1818527229116678144 |
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| author | Leandro Recova Adolfo Rumbos |
| author_facet | Leandro Recova Adolfo Rumbos |
| author_sort | Leandro Recova |
| collection | DOAJ |
| description | In this article, we study the existence and multiplicity of solutions of the
boundary-value problem
$$\displaylines{
-\Delta u = f(x,u), \quad \text{in } \Omega, \cr
u = 0, \quad \text{on } \partial\Omega,
}$$
where $\Delta$ denotes the N-dimensional Laplacian, $\Omega$ is a bounded domain
with smooth boundary, $\partial\Omega$, in $\mathbb{R}^N$ $(N\geq 3)$, and
f is a continuous function having subcritical growth in the second variable. |
| first_indexed | 2024-12-11T06:33:27Z |
| format | Article |
| id | doaj.art-cdd9f99a1b7a48a19333d161e451c674 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-11T06:33:27Z |
| publishDate | 2020-06-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-cdd9f99a1b7a48a19333d161e451c6742022-12-22T01:17:27ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912020-06-01202060,115Existence and multiplicity for a superlinear elliptic problem under a non-quadradicity condition at infinityLeandro Recova0Adolfo Rumbos1 T-Mobile Inc., Ontario, CA, USA Pomona College, Claremont, CA, USA In this article, we study the existence and multiplicity of solutions of the boundary-value problem $$\displaylines{ -\Delta u = f(x,u), \quad \text{in } \Omega, \cr u = 0, \quad \text{on } \partial\Omega, }$$ where $\Delta$ denotes the N-dimensional Laplacian, $\Omega$ is a bounded domain with smooth boundary, $\partial\Omega$, in $\mathbb{R}^N$ $(N\geq 3)$, and f is a continuous function having subcritical growth in the second variable.http://ejde.math.txstate.edu/Volumes/2020/60/abstr.htmlsemilinear elliptic boundary value problemsuperlinear subcritical growthinfinite dimensional morse theorycritical groups |
| spellingShingle | Leandro Recova Adolfo Rumbos Existence and multiplicity for a superlinear elliptic problem under a non-quadradicity condition at infinity Electronic Journal of Differential Equations semilinear elliptic boundary value problem superlinear subcritical growth infinite dimensional morse theory critical groups |
| title | Existence and multiplicity for a superlinear elliptic problem under a non-quadradicity condition at infinity |
| title_full | Existence and multiplicity for a superlinear elliptic problem under a non-quadradicity condition at infinity |
| title_fullStr | Existence and multiplicity for a superlinear elliptic problem under a non-quadradicity condition at infinity |
| title_full_unstemmed | Existence and multiplicity for a superlinear elliptic problem under a non-quadradicity condition at infinity |
| title_short | Existence and multiplicity for a superlinear elliptic problem under a non-quadradicity condition at infinity |
| title_sort | existence and multiplicity for a superlinear elliptic problem under a non quadradicity condition at infinity |
| topic | semilinear elliptic boundary value problem superlinear subcritical growth infinite dimensional morse theory critical groups |
| url | http://ejde.math.txstate.edu/Volumes/2020/60/abstr.html |
| work_keys_str_mv | AT leandrorecova existenceandmultiplicityforasuperlinearellipticproblemunderanonquadradicityconditionatinfinity AT adolforumbos existenceandmultiplicityforasuperlinearellipticproblemunderanonquadradicityconditionatinfinity |