Analysis of nontrivial radial solutions for singular superlinear [formula omitted]-Hessian equations

Abstract

We consider the singular superlinear k-Hessian problem Sk(D2u)=λH(|x|)f(−u)inΩ,u=0on∂Ω, where λ is a positive parameter, Sk(D2u) is the k-Hessian operator of u, Ω is the open unit ball in Rn, H is a positive weight function which is singular near the boundary ∂Ω, and f is a continuous function and may be singular at 0 with possible k-superlinear growth at ∞. We establish an existence result for λ small, multiplicity results of nontrivial radial solutions for certain ranges of λ. The asymptotic behavior of nontrivial radial solutions on the parameter λ is also considered.