Multiple Sign Changing Radially Symmetric Solutions in a General Class of Quasilinear Elliptic Equations

2015/02/13 by Alves, Claudianor O., Gonçalves, J. V. A., Silva, K. O.
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1502.03962

Abstract

In this paper we prove that the equation -( r^αϕ(|u'(r)|)u'(r))' = λr^γf(u(r)), ~0 0 is a real parameter and f:\bfR→\bfR is continuous, admits an infinite sequence of sign-changing solutions satisfying u'(0) =u(R) =0. The function f is required to satisfy tf(t)>0 for t≠ 0. Our technique explores fixed point arguments applied to suitable integral equations and shooting arguments. Our main result extends earlier ones in the case ϕ is in the form ϕ(t) = |t|^β for an appropriate constant γ.

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