We consider singular problems associated with the weighted anisotropic $p$-Laplace operator $$ H_{p,w}u=\text{div}(w(x)(H(\nabla u))^{p-1}\nabla H(\nabla u)), where $H$ is a Finsler-Minkowski norm and weight $w$ belongs to class of $p$-admissible weights, which may vanish or blow up near origin. discuss existence regularity properties weak solutions for mixed exponential nonlinearities. In part...

 Based on some stationary periodic solutions and stationary soliton solutions, one studies the general solution for the relative lax system, and a number of exact solutions to the Korteweg-de Vries (KdV) equation are first constructed by the known Darboux transformation, these solutions include double and triple singular periodic solutions as well as singular soliton solutions whose amplitude d...

In this paper, Lagrange interpolation in Chebyshev-Gauss-Lobatto nodes is used to develop a procedure for finding discrete and continuous approximate solutions of a singular boundary value problem. At first, a continuous time optimization problem related to the original singular boundary value problem is proposed. Then, using the Chebyshev- Gauss-Lobatto nodes, we convert the continuous time op...

We determine explicitly the Hodge ideals for determinant hypersurface as an intersection of symbolic powers determinantal ideals. prove our results by studying and weight filtrations on mixed module $$\mathcal {O}_{\mathscr {X}}(*\mathscr {Z})$$ regular functions space $$\mathscr {X}$$ $$n\times n$$ matrices, with poles along divisor {Z}$$ singular matrices. The composition factors filtration a...

<p style='text-indent:20px;'>We establish the existence of bounded very weak solutions to a large class stationary diffusive logistic equations with weights by constructing suitable sub and supersolutions. This problems corresponds case in which absorption term dominates over forcing term. The simultaneous singular nonlinearities is also considered. shows that if limitations growth popula...

We consider the Dirichlet problem for a class of elliptic and parabolic equations in upper-half space $\mathbb{R}^d_+$, where coefficients are product $x_d^\alpha, \alpha \in (-\infty, 1),$ bounded uniformly matrix coefficients. Thus, singular or degenerate near boundary $\{x_d =0\}$ they may not locally integrable. The novelty work is that we find proper weights under which existence, uniquene...

in this paper, some elementary operations on triangular fuzzynumbers (tfns) are defined. we also define some operations on triangularfuzzy matrices (tfms) such as trace and triangular fuzzy determinant(tfd). using elementary operations, some important properties of tfms arepresented. the concept of adjoints on tfm is discussed and some of theirproperties are. some special types of tfms (e.g. pu...

in the linear system ax = b the points x are sometimes constrained to lie in a given subspace s of column space of a. drazin inverse for any singular or nonsingular matrix, exist and is unique. in this paper, the singular consistent or inconsistent constrained linear systems are introduced and the effect of drazin inverse in solving such systems is investigated. constrained linear system arise ...