In this paper, we study a multi-dimensional backward stochastic differential equation with jumps (BSDEJ) that has non-Lipschitz generator and unbounded random time horizon. For any p ∈ (1,∞), we show that the BSDEJ with a p-integrable terminal condition admits a unique L-type solution.

We consider a Cauchy problem associated to a nonconvex differential inclusion with ”maxima” and we prove a Filippov type existence result. This result allows to obtain a relaxation theorem for the problem considered.

To start with, having employed transformation wave, some nonlinear partial differential equations have been converted into an ODE. Then, using the infinite series method for equations with similar linear part, the researchers have earned the exact soliton solutions of the selected equations. It is required to state that the infinite series method is a well-organized method for obtaining exact s...

the spline collocation method  is employed to solve a system of linear and nonlinear fredholm and volterra integro-differential equations. the solutions are collocated by cubic b-spline and the integrand is approximated by the newton-cotes formula. we obtain the unique solution for linear and nonlinear system $(nn+3n)times(nn+3n)$ of integro-differential equations. this approximation reduces th...

The nonlinear bending behavior of sector graphene sheets is studied subjected to uniform transverse loads resting on a Winkler-Pasternak elastic foundation using the nonlocal elasticity theory. Considering the nonlocal differential constitutive relations of Eringen theory based on first order shear deformation theory and using the von-Karman strain field, the equilibrium partial differential eq...