Existence of solutions to fully nonlinear elliptic equations with gradient nonlinearity

In this article, we study the existence and multiplicity of nontrivial solutions to the problem (formula presented) where Ω is a smooth bounded domain in ℝⁿ, n > 2. We show that the problem possesses nontrivial solutions for small value of ε provided f and ψ are continuous and f has a positive zero. We employ degree theory arguments and Liouville type theorem for the multiplicity of the solutionss.