Qixiang Dong

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This paper is concerned with a class of partial nonlocal neutral functional differential and integrodifferential equations with bounded delay in Banach spaces, which are more general than those models been studied. Some existence results of mild solutions to such problems are obtained under the conditions in respect of the Hausdorff’s measure of(More)
* Correspondence: lpzmath@yahoo. com.cn School of Mathematics, Yangzhou University, Yangzhou 225002, China Abstract This article is concerned with impulsive semilinear differential equations with nonlocal initial conditions in Banach spaces. The approach used is fixed point theorem combined with the technique of operator transformation. Existence results(More)
This paper is concerned with nonlinear fractional differential equations with the Caputo derivative. Existence results are obtained for terminal value problems and initial value problems with initial conditions at inner points. It is also proved that the sufficient condition in order that a locally closed subset be a viable domain is the tangency condition.(More)
Let X be a Banach space, A : D(A) ⊂ X → X the generator of a compact C0-semigroup S(t) : X → X, t ≥ 0, D(·) : (a, b)→ 2X a tube in X, and f : (a, b)×B → X a function of Carathéodory type. The main result of this paper is that a necessary and sufficient condition in order that D(·) be viable of the semilinear differential equation with infinite delay u′(t) =(More)
Let A be a square matrix. We construct projection-based commuting solutions of the quadratic matrix equation AXA = XAX, which are associated with nonsemisimple eigenvalues of A with at least one 1× 1 Jordan block, based on special projections onto some subspaces of the corresponding generalized eigenspaces. The result extends the main one (Applied Math.(More)
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