In this paper‎, ‎existence of an $L^p$-solution for 2DIEs (Two‎ ‎Dimensional Integral Equations) of the Hammerstein type is‎ ‎discussed‎. ‎The main tools in this discussion are Schaefer's and‎ ‎Schauder's fixed point theorems with a general version of‎ ‎Gronwall's inequality‎.

Many time-varying phenomena of various fields in science and engineering can be modeled as a stochastic differential equations, so investigation of conditions for existence of solution and obtain the analytical and numerical solutions of them are important. In this paper, the Adomian decomposition method for solution of the stochastic differential equations are improved.  Uniqueness and converg...

in the present paper an operator-differential equation of second order in complex domain isconsidered when the coefficients have singularity of pole type at the point z=0. a theorem of existence of thesolution of the equation is proved and the spectral property of the solution is separately investigated when thecoefficients are spectral operators.