Positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation in a ball
Keywords
Quasilinear elliptic differential equation, Minkowski-curvature, Dirichlet boundary condition, radial solution, positive solution, existence, multiplicity, variational methodsAbstract
We study the existence and multiplicity of positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation $$ \cases \displaystyle -\text{\rm div}\bigg( \frac{\nabla v} {\sqrt{1 - |\nabla v|^2}}\bigg)= f(|x|,v) &\quad \text{in } B_R, \\ \displaystyle v=0 & \quad \text{on } \partial B_R, \endcases $$ < p> where $B_R$ is a ball in $\mathbb{R}^N$ ($N\ge 2$). According to the behaviour of $f=f(r,s)$ near $s=0$, we prove the existence of either one, two or three positive solutions. All results are obtained by reduction to an equivalent non-singular one-dimensional problem, to which variational methods can be applied in a standard way.Downloads
Published
2016-04-12
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COELHO, Isabel, CORSATO, Chiara and RIVETTI, Sabrina. Positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation in a ball. Topological Methods in Nonlinear Analysis. Online. 12 April 2016. Vol. 44, no. 1, pp. 23 - 39. [Accessed 14 December 2024].
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