Existence of countably many p-k-convex solutions for p-k-Hessian equations and systems

This paper analyzes, by employing topological approaches, the solvability of equations and systems involving p-k-Hessian operator. We first provide sufficient conditions for the existence of infinitely many p-k-convex solutions for a p-k-Hessian equation. Then we discuss the existence of infinitely many p-k-convex solutions for a p-k-Hessian system. We also study the existence of three infinite families of p-k-convex solutions for p-k-Hessian equations and systems. An example is presented to illustrate the applicability of our main results.