Alfonso Castro, Jorge Cossio, Sigifredo Herron, Carlos Velez
Abstract:
We prove the existence of infinitely many sign-changing radial solutions for a
Dirichlet problem in a ball defined by the p-Laplacian operator perturbed
by a nonlinearity of the form W(|x|)g(u), where the
weight function W changes sign exactly once, W(0)<0, W(1) > 0, and function
g is p-superlinear at infinity.
Standard phase plane analysis arguments do not apply here because the solutions
to the corresponding initial value problem may blow up in the region where the
weight function is negative. Our result extend those in [2]
where W is assumed to be positive at 0 and negative at 1.
Published October 6, 2021.
Math Subject Classifications: 35J92, 34B15, 34G20.
Key Words: Indefinite weight; p-Laplace operator; phase plane;
radial solution; shooting method; distributional solution.
DOI: https://doi.org/10.58997/ejde.sp.01.c2
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Alfonso Castro Department of Mathematics Harvey Mudd College Claremont, CA 91711, USA email: castro@g.hmc.edu |
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Jorge Cossio Escuela de Matemáticas Universidad Nacional de Colombia Sede Medellín Medellín, Colombia \email: jcossio@unal.edu.co |
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Sigifredo Herrón Escuela de Matemáticas Universidad Nacional de Colombia Sede Medellín Medellín, Colombia \email{sherron@unal.edu.co |
| Carlos Vélez Escuela de Matemáticas Universidad Nacional de Colombia Sede Medellín Medellíin, Colombia email: cauvelez@unal.edu.co |
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