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By using the method of successive approximation, we prove the existence and uniqueness of a solution of the fuzzy differential equation x (t) = f (t, x(t)), x(t 0) = x 0. We also consider an-approximate solution of the above fuzzy differential equation.
We investigate the existence and uniqueness of solutions of the following equation of hyperbolic type with a strong dissipation: utt(t,x)− ( α+β (∫ Ω |∇u(t,y)|2dy )γ) ∆u(t,x) −λ∆ut(t,x)+μ|u(t,x)|q−1u(t,x)= 0, x ∈Ω, t ≥ 0, u(0,x)=u0(x), ut(0,x)=u1(x), x ∈Ω, u|∂Ω = 0, where q > 1, λ > 0, μ ∈R, α, β≥ 0, α+β > 0, and ∆ is the Laplacian in RN .
By using a fixed-point theorem in G-convex spaces due to the first author, an existence result for abstract nonlinear inequalities without any monotonicity assumptions is established. As a consequence of our result, we obtain some further generalizations of recent known results. As application, an existence theorem for perturbed saddle point problems is… (More)
In this paper, we prove the existence of mild and strong solutions of nonlinear time varying delay integrodifferential equations of Sobolev type with nonlocal cqnditions in Banach spaces. The results are obtained by using the theory of compact semigroups and Schaefer's fixed-point theorem .