Topological methods for boundary value problems involving discrete vector $\phi$-Laplacians
Keywords
Boundary value problems, Brouver degreeAbstract
In this paper, using Brouwer degree arguments, we prove some existence results for nonlinear problems of the type $$ -\nabla[\phi(\Delta x_m)]=g_m(x_m,\Delta x_m) \quad (1\leq m\leq n-1), $$ submitted to Dirichlet, Neumann or periodic boundary conditions, where $\phi(x)=|x|^{p-2}x$ $(p> 1)$ or $\phi(x)={x}/{\sqrt{1-|x|^2}}$ and $g_m\colon \mathbb{R}^N\to\mathbb{R}^N$ $(1\leq m\leq n-1)$ are continuous nonlinearities satisfying some additional assumptions.Downloads
Published
2011-04-23
How to Cite
1.
BEREANU, Cristian and GHEORGHE, Dana. Topological methods for boundary value problems involving discrete vector $\phi$-Laplacians. Topological Methods in Nonlinear Analysis. Online. 23 April 2011. Vol. 38, no. 2, pp. 265 - 276. [Accessed 4 December 2024].
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