Existence of Solutions for a Class of Gradient Fractional Elliptic Equation
By using the mountain pass theorem and iterative methods to prove that the existence of positive solutions to the following frac-tional elliptic equation:{(-Δ)spu+V(x)up-2u = f(u,|▽u|p-2 ▽u),u ∈ Xs(RN),u(x)>0,∀x ∈RN.Where 1<p<N,N≥2,0<s<1,(-Δ)sp is the fractional p-Laplacian operator,the nonlinear termf:R×RN→Ris a continuous funtion which depends on the gradient term of the solution,V(x)is a positive continuous function.
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