In this paper, we discuss the existence and uniqueness of mild solutions of random impulsive abstract neutral partial differential equations in a real separable Hilbert space. The results are obtained by using Leray-S...In this paper, we discuss the existence and uniqueness of mild solutions of random impulsive abstract neutral partial differential equations in a real separable Hilbert space. The results are obtained by using Leray-Schauder Alternative and Banach Contraction Principle.Finally an example is given to illustrate our problem.展开更多
The aim of this paper is to study singular dynamics of solutions of Camassa-Holm equation. Based on the semigroup theory of linear operators and Banach contraction mapping principle, we prove the asymptotic stability ...The aim of this paper is to study singular dynamics of solutions of Camassa-Holm equation. Based on the semigroup theory of linear operators and Banach contraction mapping principle, we prove the asymptotic stability of the explicit singular solution of Camassa-Holm equation.展开更多
In this research collection,we estimate the existence of the unique solution for the boundary value problem of nonlinear fractional q-difference equation having the given form c D^(ζ)_(q) v(t)−h(t,v(t))=0,0≤t≤1,α_...In this research collection,we estimate the existence of the unique solution for the boundary value problem of nonlinear fractional q-difference equation having the given form c D^(ζ)_(q) v(t)−h(t,v(t))=0,0≤t≤1,α_(1)v(0)+β_(1)D_(q)v(0)=v(η1),α_(2)v(1)−β_(2)D_(q)v(1)=v(η2),where 1<ζ≤2,(η1,η2)∈(0,1)^(2),α_(i),β_(i)∈R(i=1,2),h∈C([0,1]×R,R)and c Dζq represents the Caputo-type nonclassical q-derivative of orderζ.We use well-known principal of Banach contraction,and Leray–Schauder nonlinear alternative to vindicate the unique solution existence of the given problem.Regarding the applications,some examples are solved to justify our outcomes.展开更多
文摘In this paper, we discuss the existence and uniqueness of mild solutions of random impulsive abstract neutral partial differential equations in a real separable Hilbert space. The results are obtained by using Leray-Schauder Alternative and Banach Contraction Principle.Finally an example is given to illustrate our problem.
文摘The aim of this paper is to study singular dynamics of solutions of Camassa-Holm equation. Based on the semigroup theory of linear operators and Banach contraction mapping principle, we prove the asymptotic stability of the explicit singular solution of Camassa-Holm equation.
文摘In this research collection,we estimate the existence of the unique solution for the boundary value problem of nonlinear fractional q-difference equation having the given form c D^(ζ)_(q) v(t)−h(t,v(t))=0,0≤t≤1,α_(1)v(0)+β_(1)D_(q)v(0)=v(η1),α_(2)v(1)−β_(2)D_(q)v(1)=v(η2),where 1<ζ≤2,(η1,η2)∈(0,1)^(2),α_(i),β_(i)∈R(i=1,2),h∈C([0,1]×R,R)and c Dζq represents the Caputo-type nonclassical q-derivative of orderζ.We use well-known principal of Banach contraction,and Leray–Schauder nonlinear alternative to vindicate the unique solution existence of the given problem.Regarding the applications,some examples are solved to justify our outcomes.
