Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1220.45009
Yan, Zuomao
Existence of solutions for nonlocal impulsive partial functional integrodifferential equations via fractional operators. (English)
[J] J. Comput. Appl. Math. 235, No. 8, 2252-2262 (2011). ISSN 0377-0427

The paper deals with the following partial functional integro-differential equation: $$\multline x'(t) = Ax(t) + F\left(t,\,x(\sigma_1(t)),\,\dots,\,x(\sigma_n(t)),\int_0^t h(t,\,s,\,x(\sigma_{n+1}(s)))ds\right),\\ t\in [0,\,b],\,t\ne t_k,\; k=\overline{1,\,m}, \endmultline$$ where $A$ is the infinitesimal generator of a compact, analytic semigroup, $t_k\in [0,\,b]$, and $F,\,h,\,\sigma_k$ are some given functions. The equation is considered here together with the conditions: $$x(0) + g(x) = x_0\;\;\text { and }\;\;\; x(t_k^+) - x(t_k^-) = I_k(x(t_k)),\;\; k=\overline{1,\,m}.$$ It is shown that, under suitable conditions on the functions $F,\,h,\,g,\,\sigma_k$, and for any $x_0\in X^{\alpha}$, the above Cauchy problem has at least one mild solution on $[0,\,b]$. The proof of this result employs the Leray-Schauder alternative. The author also presents an illustrative example at the end of the paper.
[Iulian Stoleriu (Iaşi)]

MSC 2000:: *45J05 Integro-ordinary differential equations
45G10 Nonsingular nonlinear integral equations
26A33 Fractional derivatives and integrals (real functions)

Keywords: impulsive partial functional integro-differential equations; fixed point; analytic semigroup; nonlocal conditions; Cauchy problem; mild solution; Leray-Schauder alternative

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]