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 −Δpu=|u|δ−1u in B(0,1)∖{0}⊂RN,\, u=0 for |x|=1, where N>p>1 and δ>p−1. Solutions are characterized by their nodal properties. The case δ+1<NpN−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.

Dalbono, F., & García-Huidobro, M. (2005). Singular solutions to a quasilinear ODE. ADVANCES IN DIFFERENTIAL EQUATIONS, 10(7), 747-765.

Singular solutions to a quasilinear ODE

DALBONO, Francesca;
2005

Abstract

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 −Δpu=|u|δ−1u in B(0,1)∖{0}⊂RN,\, u=0 for |x|=1, where N>p>1 and δ>p−1. Solutions are characterized by their nodal properties. The case δ+1
Dalbono, F., & García-Huidobro, M. (2005). Singular solutions to a quasilinear ODE. ADVANCES IN DIFFERENTIAL EQUATIONS, 10(7), 747-765.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/64879
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