Singular solutions to a quasilinear ODE

DALBONO, F; García Huidobro, M

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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.

Data di pubblicazione:	2005
Titolo:	Singular solutions to a quasilinear ODE
Autori:	DALBONO, Francesca García Huidobro, M. mostra contributor esterni nascondi contributor esterni
Citazione:	Dalbono, F., & García Huidobro, M. (2005). Singular solutions to a quasilinear ODE. ADVANCES IN DIFFERENTIAL EQUATIONS, 10(7), 747-765.
Rivista:	ADVANCES IN DIFFERENTIAL EQUATIONS
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<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.
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http://hdl.handle.net/10447/64879

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