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This paper deals with the existence of solutions of the elliptic equation with nonlinear gradient term −Δu=f(x,u,∇u) on Ω restricted by the boundary condition u|∂Ω=0, where Ω is a bounded… Click to show full abstract
This paper deals with the existence of solutions of the elliptic equation with nonlinear gradient term −Δu=f(x,u,∇u) on Ω restricted by the boundary condition u|∂Ω=0, where Ω is a bounded domain in RN with sufficiently smooth boundary ∂Ω, N≥2, and f:Ω¯×R×RN→R is continuous. The existence results of classical solutions and positive solutions are obtained under some inequality conditions on the nonlinearity f(x,ξ,η) when |(ξ,η)| is small or large enough.
Keywords:
solutions nonlinear;
elliptic equations;
nonlinear elliptic;
classical solutions;
existence classical;
equations gradient
Journal Title: Entropy
Year Published: 2022
Link to full text (if available)
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Journal Title: Entropy
Year Published: 2022
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!