کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
841812 908520 2011 21 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Resolvents and solutions of weakly singular linear Volterra integral equations
موضوعات مرتبط
مهندسی و علوم پایه سایر رشته های مهندسی مهندسی (عمومی)
پیش نمایش صفحه اول مقاله
Resolvents and solutions of weakly singular linear Volterra integral equations
چکیده انگلیسی

The structure of the resolvent R(t,s)R(t,s) for a weakly singular matrix function B(t,s)B(t,s) is determined, where B(t,s)B(t,s) is the kernel of the linear Volterra vector integral equation equation(E )x(t)=a(t)+∫0tB(t,s)x(s)ds and a(t)a(t) is a given continuous vector function. Using contraction mappings in a Banach space of continuous vector functions with an exponentially weighted norm, we show that when B(t,s)B(t,s) satisfies certain integral conditions, R(t,s)R(t,s) has the form R(t,s)=B(t,s)+R1(t,s),R(t,s)=B(t,s)+R1(t,s), where R1(t,s)R1(t,s) is the unique continuous solution of the integral equation R1(t,s)=B1(t,s)+∫stB(t,u)R1(u,s)du and B1(t,s)B1(t,s) is defined by B1(t,s):=∫stB(t,u)B(u,s)du. As examples, the formulas of resolvents for a couple of weakly singular kernels of practical interest are derived. We also obtain conditions under which a weakly singular integral equation (E) has a unique continuous solution x(t)x(t) and show that it can be expressed in terms of R(t,s)R(t,s) by x(t)=a(t)+∫0tR(t,s)a(s)ds. Finally, we show that there are parallel results for an alternative resolvent R˜(t,s) and examine when it and R(t,s)R(t,s) are equivalent.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Nonlinear Analysis: Theory, Methods & Applications - Volume 74, Issue 5, 1 March 2011, Pages 1892–1912
نویسندگان
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