‎in the present paper we investigate the $l_1$-weak ergodicity of‎ ‎nonhomogeneous continuous-time markov processes with general state‎ ‎spaces‎. ‎we provide a necessary and sufficient condition for such‎ ‎processes to satisfy the $l_1$-weak ergodicity‎. ‎moreover‎, ‎we apply‎ ‎the obtained results to establish $l_1$-weak ergodicity of quadratic‎ ‎stochastic processes‎.

After the successful applications of the combination of the method of fundamental solutions (MFS), the method of particular solutions (MPS), and the eigenfunctions expansion method (EEM) to solve 2D homogeneous and nonhomogeneous diffusion equations by Young et al. (Young et al., Numer Meth Part Differ Equat 22 (2006), 1173), this article intends to extend the same fundamental concepts to calcu...

The existence of infinitely many solutions is established for a class of nonlinear functionals involving the p-biharmonic operator with nonhomoge- neous Neumann boundary conditions. Using a recent critical-point theorem for nonsmooth functionals and under appropriate behavior of the nonlinear term and nonhomogeneous Neumann boundary conditions, we obtain the result.

Keywords: Positive solutions Third-order three-point BVPs Nonhomogeneous Fixed point theorem Existence and nonexistence a b s t r a c t In this work, by employing the Guo–Krasnosel'skii fixed point theorem and Schauder's fixed point theorem, we study the existence and nonexistence of positive solutions to the third-order three-point nonhomogeneous boundary value problem u (t) + a(t)f (u(t)) = 0...