Existence of solutions to fully nonlinear elliptic equations with gradient nonlinearity

Tyagi, JagmohanJagmohanTyagiVerma, Ram BaranRam BaranVerma2025-08-302025-08-302017-10-0110.11650/tjm/79742-s2.0-85031089776https://d8.irins.org/handle/IITG2025/22379In this article, we study the existence and multiplicity of nontrivial solutions to the problem (formula presented) where Ω is a smooth bounded domain in ℝ<sup>n</sup>, 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.trueDegree theory | Fully nonlinear elliptic equations | Liouville type theorem | Viscosity solutionExistence of solutions to fully nonlinear elliptic equations with gradient nonlinearityArticlehttps://doi.org/10.11650/tjm/79741037-1056October 20171arJournal1WOS:000412786200005