Eigenvalue problems for singular p-Monge-Ampère equations

Abstract

Using the eigenvalue theory of completely continuous operators, we are concerned with the determining values of μ, in which there are nontrivial radial solutions to the singular p-Monge-Ampère problem{det(D(|Du|p−2Du))=μh(|x|)f(−u)inΩ,u=0on∂Ω, where μ>0 is a parameter, Ω is the open unit ball in Rn. In addition, as an application, we derive some criteria for the existence of nontrivial radial solutions to the power-type problem of p-Monge-Ampère equations. The dependence of nontrivial radial solution uμ on the parameter μ is also considered.