6533b858fe1ef96bd12b6357
RESEARCH PRODUCT
Singular solutions to a quasilinear ODE
Francesca DalbonoM. Garcia-huidobrosubject
Applied Mathematics34B1634B15Singular solutions superlinear problem multiplicity result p-Laplacian equation rotation number radial solutionsAnalysis35J60description
In this paper, we prove the existence of infinitely many radial solutions having a singular behaviour at the origin for a superlinear problem of the form $-\Delta_pu=|u|^{\delta-1}u$ in $B(0,1)\setminus\{0\}\subset\mathbb R^N$,\, $u=0$ for $|x|=1$, where $N>p>1$ and $\delta>p-1$. Solutions are characterized by their nodal properties. The case $\delta+1 <\frac{Np}{N-p}$ is treated. The study of the singularity is based on some energy considerations and takes into account the classification of the behaviour of the possible solutions available in the literature. By following a shooting approach, we are able to deduce the main multiplicity result from some estimates on the rotation numbers associated to the solutions.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2005-01-01 |