Multiple Sign Changing Radially Symmetric Solutions in a General Class of Quasilinear Elliptic Equations
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 $f:{\bf{R}}\to{\bf{R}}$ 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\neq 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 $γ$.
math.AP↗