In this work, we conduct a comparative study among the combine Laplace transform and modied Adomian decomposition method (LMADM) and two traditional methods for an analytic and approximate treatment of special type of nonlinear Volterra integro-differential equations of the second kind. The nonlinear part of integro-differential is approximated by Adomian polynomials, and the equation is reduce...

In this paper, we develop new methods of solving the Poincaré-Lelong equation. It is mainly via the study of the large time asymptotics of a global solution to the Hodge-Laplace heat equation on (1, 1)-forms. The method is shown to be effective through obtaining better, sometimes optimal, existence results for the Poincaré-Lelong equation.

We show that bounded solutions of the quasilinear elliptic equation \(\Delta_{p(x)} u=g+div(\textbf{F})\) are locally Hölder continuous provided functions \(g\) and \(\textbf{F}\) in suitable Lebesgue spaces.

We consider a $ p $-Laplace evolution problem with stochastic forcing on bounded domain D\subset\mathbb{R}^d homogeneous Dirichlet boundary conditions for 1<p<\infty $. The additive noise term is given by integral in the sense of Itô. technical difficulties arise from merely integrable random initial data u_0 under consideration. Due to poor regularity data, estimates W^{1,p}_0(D) are ava...