Related papers: The accessory parameter problem in positive charac…
We get stationary solutions of a free stochastic partial differential equation. As an application, we prove equality of non-microstate and microstate free entropy dimensions under a Lipschitz like condition on conjugate variables, assuming…
As is known, the problems for the differential equations with continuously changing order of the derivatives are not considered completely. In this paper we consider the initial and boundary value problems for this type of linear ordinary…
In the present paper, by using variational method, the existence of non-trivial solutions to an anisotropic discrete non-linear problem involving p(k)-Laplacian operator with Dirichlet boundary condition is investigated. The main technical…
The momentous objective of this work is to discuss some qualitative properties of solutions such as the estimate on the solutions, the continuous dependence of the solutions on initial conditions as well as the existence and uniqueness of…
This note presents absolute bounds on the size of the coefficients of the characteristic and minimal polynomials depending on the size of the coefficients of the associated matrix. Moreover, we present algorithms to compute more precise…
We consider a nonlinear Dirichlet problem driven by the $(p,q)$-Laplacian with $1<q<p$. The reaction is parametric and exhibits the competing effects of a singular term and of concave and convex nonlinearities. We are looking for positive…
We prove the existence and uniqueness of weak solution of a Neumann boundary problem for an elliptic partial differential equation (PDE for short) with a singular divergence term which can only be understood in a weak sense. A probabilistic…
This paper is devoted to the study of the singularly perturbed second order partial integro-differential equations. The estimation of the solutions of Cauchy problem is obtained.
The aim of the present paper is to study the existence, uniqueness and some other properties of solutions of a certain partial dynamic integrodifferential equations. The Banach fixed point theorem and certain fundamental inequality with…
The problem "A general characterization of uniqueness polynomial for non-critically injective polynomials" has been remained open since the last two decades. In this paper, we explore this open problem. To this end, we initiate a new…
We consider linear n-th order stochastic differential equations on [0,1], with linear boundary conditions supported by a finite subset of [0,1]. We study some features of the solution to these problems, and especially its conditional…
We study generalized fractional $p$-Laplacian equations to prove local boundedness and H\"older continuity of weak solutions to such nonlocal problems by finding a suitable fractional Sobolev-Poincar\'e inquality.
In this paper, we consider the existence of solutions of the following nonhomogeneous fractional $p(x,.)$-Laplacian Dirichlet problem: \begin{equation*} \left\{\begin{aligned} \Big(-\Delta_{p(x,.)}\Big)^s u (x)&=f(x, u) &\text { in }&…
For a general one-sided nonautonomous dynamics defined by a sequence of linear operators, we consider the notion of a polynomial dichotomy with respect to a sequence of norms and we characterize it completely in terms of the admissibility…
We investigate the existence of solutions of constrained nonlinear differential inclusions with nonlocal boundary conditions. Our viability theorems are based on the assumption that the right-hand side of differential inclusion is defined…
We present a numerical method to compute accessory parameters of the uniformizing differential equations of elliptic curves associated to arithmetic Fuchsian $(1;e)$ groups. Up to $PSL_2(\bbr)$ conjugation there are only finitely many such…
We give an implicit equation for the accessory parameter on the torus which is the necessary and sufficient condition to obtain the monodromy of the conformal factor. It is shown that the perturbative series for the accessory parameter in…
We consider a Dirichlet type problem for a nonlinear, nonlocal equation driven by the degenerate fractional p-Laplacian, whose reaction combines a sublinear term depending on a positive parameter and an asymmetric perturbation (superlinear…
In this PhD thesis we introduce a generalized fractional calculus of variations. We consider variational problems containing generalized fractional integrals and derivatives, and study them using standard (indirect) and direct methods. In…
We consider a system of semi-linear partial differential equations with measurable coefficients and a nonlinear Neumann boundary condition. We then construct a sequence of penalized partial differential equations which converges to a…