Existence of entire solutions for semilinear elliptic problems on ${\mathbb R}^{N}$
Keywords
Nonlinear elliptic problem, positive solution, entire solutionAbstract
In this paper, we consider the existence of positive and negative entire solutions of semilinear elliptic problem $$ -\Delta u + u = g(x,u), \quad u \in H^{1}({\mathbb R}^{N})\tag{P} $$ where $N \geq 2$ and $g:{\mathbb R}^{N} \times {\mathbb R }\to {\mathbb R}$ is a continuous function with superlinear growth and $g(x,0) = 0$ on ${\mathbb R}^{N} $.Downloads
Published
1999-03-01
How to Cite
1.
HIRANO, Norimichi. Existence of entire solutions for semilinear elliptic problems on ${\mathbb R}^{N}$. Topological Methods in Nonlinear Analysis. Online. 1 March 1999. Vol. 13, no. 1, pp. 1 - 15. [Accessed 19 April 2024].
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