Nontrivial solutions for multiparameter k -Hessian systems

AbstractThis paper is devoted to studying the coupled system of multiparameter k-Hessian equationswhere B = {x ∈ ℝn : |x| < 1}, λ1, λ2 are positive parameters, ρi(i = 1, 2) is singular near the boundary ∂B, fi(i = 1, 2) satisfies a combined superlinear condition at ∞. Employing the fixed point theorem of Krasnosel'skii type in Banach space, the existence and multiplicity of nontrivial radial solutions are established. In particular, the dependence of the solutions on the parameters λ1, λ2 is also discussed. Finally, we study the nonexistence results of nontrivial radial solutions for the case λ1, λ2 ≫ 1.Mathematics Subject Classification (2020): 34B1534B18Key words: Coupled k-Hessian equationsnontrivial radial solutionexistencemultiplicity and nonexistencefixed point theorem of Krasnosel'skii type