in this paper, we present a method for solving the rst kind abel integral equation. in thismethod, the rst kind abel integral equation is transformed to the second kind volterraintegral equation with a continuous kernel and a smooth deriving term expressed by weaklysingular integrals. by using sidi's sinm - transformation and modied navot-simpson'sintegration rule, an algorithm for...

We are concerning with a nonlinear Hammerstein quadratic integral equation. We prove the existence of at least one positive solution x ∈ L1 under Carathèodory condition. Secondly we will make a link between Peano condition and Carathèodory condition to prove the existence of at least one positive continuous solution. Finally the existence of the maximal and minimal solutions will be proved.

We are concerned here with the existence of at least one positive continuous solution of the quadratic integral equation of fractional orders x(t) = a(t) + If(t, x(t)) · Ig(t, x(t)), α, β ∈ (0, 1]. The maximal and minimal solutions are also proved. Some applications are given.

A construction of the heat kernel diagonal is considered as element of generalized Zeta function, that, being meromorfic function, its gradient at the origin defines determinant of a differential operator in a technique for regularizing quadratic path integral. Some classes of explicit expression in the case of finite-gap potential coefficient of the heat equation are constructed.

The quantum dynamical systems of identical particles admitting an additional integral quadratic in momenta are considered. It is found that an appropriate ordering procedure exists which allows to convert the classical integrals into their quantum counterparts. The relation to the separation of variables in Schroedinger equation is discussed. supported by KBN grant 5 P03B06021 supported by KBN ...

We prove an existence theorem of monotonic solutions for a quadratic integral equation of Fredholm-Stieltjes type in C[0, 1]. The concept of measure of noncompactness and a fixed point theorem due to Darbo are the main tools in carrying out our proof.

The quantum dynamical systems of identical particles admitting an additional integral quadratic in momenta are considered. It is found that an appropriate ordering procedure exists which allows to convert the classical integrals into their quantum counterparts. The relation to the separation of variables in Schroedinger equation is discussed. supported by KBN grant 5 P03B06021 supported by KBN ...

We present an existence theorem for at least one continuous solution for a nonlinear quadratic functional integral equation of fractional (arbitrary) order. Also, we prove the existence of maximal and minimal solutions for that equations. 2000 Mathematics Subject Classification: 32A55; 11D09

in this paper, existence theorems for the fuzzy volterra-fredholm integral equations of mixed type (fvfiemt) involving fuzzy number valued mappings have been investigated. then, by using banach's contraction principle, sufficient conditions for the existence of a unique solution of fvfiemt are given. finally, illustrative examples are presented to validate the obtained results.