‎in this study‎, ‎properties of spectral characteristic are investigated for‎ ‎singular sturm-liouville operators in the case where an eigen‎ ‎parameter not only appears in the differential equation but is‎ ‎also linearly contained in the jump conditions‎. ‎also weyl function‎ ‎for considering operator has been defined and the theorems which‎ ‎related to uniqueness of solution of inverse proble...

this paper presents a comparison between variational iteration method (vim) and modfied variational iteration method (mvim) for approximate solution a system of volterra integral equation of the first kind. we convert a system of volterra integral equations to a system of volterra integro-di®erential equations that use vim and mvim to approximate solution of this system and hence obtain an appr...

‎we study dual integral equations which appear in formulation of the‎ ‎potential distribution of an electrified plate with mixed boundary‎ ‎conditions‎. ‎these equations will be converted to a system of‎ ‎singular integral equations with cauchy type kernels‎. ‎using‎ ‎chebyshev polynomials‎, ‎we propose a method to approximate the‎ ‎solution of cauchy type singular integral equation which will ...

generally leads to a functional differential equation for f(x) and an associated inequality. It is only occasionally that the equation forf(x) reduces to a differential equation but it may sometimes reduce to a simple functional equation or difference equation. The analysis is easily extended by replacing the substitution z = x + r by some other substitution z = s(x) which transforms the range ...

Keywords: Stefan problem Non-classical heat equation Free boundary problem Similarity solution Nonlinear heat sources Volterra integral equation a b s t r a c t We prove the existence and uniqueness, local in time, of the solution of a one-phase Stefan problem for a non-classical heat equation for a semi-infinite material with a convective boundary condition at the fixed face x = 0. Here the he...

In this paper, we present an approximate method to solve the solution of the second kind Volterra integral equations. This method is based on a previous scheme, applied by Maleknejad ‎et al., ‎‎[K. Maleknejad ‎and Aghazadeh, Numerical solution of Volterra integral equations of the second kind with convolution kernel by using Taylor-series expansion method, ‎Appl. Math. Comput.‎ (2005)]‎ to gain...

We apply the Kurzweil-Henstock integral setting to prove a Fredholm Alternative-type result for the integral equation x (t)− K Z [a,b] α (t, s)x (s) ds = f (t) , t ∈ [a, b] , where x and f are Kurzweil integrable functions (possibly highly oscillating) defined on a compact interval [a, b] of the real line with values on Banach spaces. An application is given.

By making use of asymptotic properties of nonoscillatory solutions the oscillation behavior of solutions for the integro-dynamic equation x(t) = e(t) − ∫ t 0 k(t, s)f(s, x(s))∆s, t ≥ 0 and the integral equation x(t) = e(t) − ∫ t 0 k(t, s)f(s, x(s))∆s, t ≥ 0 on time-scales are investigated. Easily verifiable sufficient conditions are established for the oscillation of all solutions. The results ...