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 |
| Summary: | 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. |
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| ISSN: | 1072-6691 |