In this article, we study the existence and uniqueness of distributional solution for semilinear fractional problems of Dirichlet form involving new operator. By means of the Leray–Schauder degree theory, we establish the existence results, with suitable assumptions on the semilinear term g and the contraction principle to prove the uniqueness in a particular case, then the numerical study of this problem using the finite difference method.
In this article, we study the existence of a weak solutions for the nonlinear fractional elliptic systems with Dirichlet boundary conditions in three cases. We use the Leray-Schauder degree and some sufficient conditions for the solvability of a resonance and non-resonance systems with respect to the spectrum of the fractional Laplacian.
In this article, we study the existence of positive solutions for the quasilinear elliptic system −∆_p u(x) = f_1(x, v(x)) + h_1(x) in Ω,−∆_p v(x) = f_2(x, u(x)) + h_2(x) in Ω,u = v = 0 on ∂Ω,where f_i(x, s), (i = 1, 2) locates between the first and the second eigenvalues of the p-Laplacian. To prove the existence of solutions, we use a topological method the Leray-Schauder degree.
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