in this paper‎, ‎we consider the following kirchhoff-type equations‎: ‎$-‎left(a+bint_{mathbb{r}^{3}}|nabla u|^{2}right)delta u+v(x) u=lambda$ $f(x,u)+u^{5}‎, ‎quad mbox{in }mathbb{r}^{3},$ ‎$u(x)>0‎, ‎quad mbox{in }mathbb{r}^{3},$ ‎$uin h^{1}(mathbb{r}^{3})‎ ,‎$ ‎ ‎‎‎where $a,b>0$ are constants and $lambda$ is a positive parameter‎. ‎the aim of this paper is to study the existence of positive ...

we show how daubechies wavelets are used to solve kuramoto-sivashinsky type equations with periodic boundary condition‎. ‎wavelet bases are used for numerical solution of the kuramoto-sivashinsky type equations by galerkin method‎. ‎the numerical results in comparison with the exact solution prove the efficiency and accuracy of our method‎.

‎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 ...

this paper describes an approximating solution, based on lagrange interpolation and spline functions, to treat functional integral equations of fredholm type and volterra type. this method can be extended to functional dierential and integro-dierential equations. for showing eciency of the method we give some numerical examples.

In this work we introduce the notion of fuzzy volterra dierence equations and study the dynamicalproperties of some classes of this type of equations. We prove some comparison theorems for theseequations in terms of ordinary volterra dierence equations. Using these results the stability of thefuzzy nonlinear volterra dierence equations is investigated.

in this paper we investigate the existence and uniqueness for volterra-fredholm type integral equations and extension of this type of integral equations. the result is obtained by using the  coupled fixed point theorems in the framework of banach space $ x=c([a,b],mathbb{r})$. finally, we  give an example to illustrate the applications of our results.

in this work, a new iterative method is proposed for obtaining the approximate solution of a class of hammerstein type integral equations system. the main structure of this method is based on the richardson iterative method for solving an algebraic linear system of equations. some conditions for existence and unique solution of this type equations are imposed. convergence analysis and error bou...

A type of nonlinearity in vibrational engineering systems emerges when the restoring force is a nonlinear function of displacement. The derivative of this function is known as stiffness. If the stiffness increases by increasing the value of displacement from the equilibrium position, then the system is known as hardening type oscillator and if the stiffness decreases by increasing the value of ...