Related papers: Existence uniqueness for a class of Nonlinear Disc…
In this paper, we discuss differentiation of solutions to the boundary value problem $y^{(n)} = f(x, y, y^{'}, y^{''}, \ldots, y^{(n-1)}), \; a<x<b,\; y^{(i)}(x_j) = y_{ij},\; 0\leq i \leq m_j, \; 1 \leq j \leq k-1$, and $y^{(i)}(x_k) +…
We prove existence of positive solutions to a boundary value problem depending on discrete fractional operators. Then, corresponding discrete fractional Lyapunov-type inequalities are obtained.
In this paper, we study the existence of positive solutions of a three-point integral boundary value problem (BVP) for the following second-order differential equation \begin{equation*} \begin{gathered} {u^{\prime \prime }}(t)+\lambda…
This work is concerned with the existence and uniqueness of boundary value problems defined on semi-infinite intervals. These kinds of problems seldom admit exactly known solutions and, therefore, the theoretical information on their…
We investigate an initial-(periodic-)boundary value problem for a continuum equation, which is a model for motion of grain boundaries based on the underlying microscopic mechanisms of line defects (disconnections) and integrated the effects…
This paper investigates the existence of solutions for a class of nonlinear higher-order dynamic equations subject to mixed boundary conditions. We consider boundary value problems in which the nonlinear reaction functions satisfy…
Using direct variational method we consider the existence of non-spurious solutions to the following Dirichlet problem $\ddot{x}\left( t\right) =f\left( t,x\left( t\right) \right) $, $x\left( 0\right) =x\left( 1\right) =0 $ where $f:\left[…
In this paper we obtain existence results for the positive solution of a singular elliptic boundary value problem. To prove the main results we use comparison arguments and the method of sub-super solutions combined with a procedure which…
In this paper, we studied the sufficient conditions for the existence of positive solutions to the boundary value problems of Caputo fractional difference equations depending on parameters with non local boundary conditions. We construct…
In this paper, we used some theorems of fixed point for studying the results of Existence and Uniqueness For Hilfer-Hadamard-Type Fractional Differential Equations, \[_{H}D^{\alpha,\beta}x(t)+f(t,x(t))=0, ~~~~~~ on~~the~~ interval~~…
The existence of stationary radial solutions to a partial differential equation arising in the theory of epitaxial growth is studied. Our results depend on the size of a parameter that plays the role of the velocity at which mass is…
We consider a problem of finding vanishing at infinity $C^1([0,\oo))$-solutions to non-homogeneous system of linear ODEs which has the pole of first order at $x=0$. The resonant case where the corresponding homogeneous problem has…
We prove existence, uniqueness and regularity results for mixed boundary value problems associated with fully nonlinear, possibly singular or degenerate elliptic equations. Our main result is a global H\"older estimate for solutions,…
In this paper, the existence of positive solutions for a nonlinear fourth-order two-point boundary value problem with integral condition is investigated. By using Krasnoselskii's fixed point theorem on cones, sufficient conditions for the…
We show an existence of a weak solution of a degenerate and/or singular semilinear elliptic boundary value (nonhomogeneous) problem lying between a given weak subsolution and a given weak supersolution. It has been applied for an existence…
We investigate linear boundary value problems for first-order one-dimensional hyperbolic systems in a strip. We establish conditions for existence and uniqueness of bounded continuous solutions. For that we suppose that the non-diagonal…
This paper presents high-order numerical methods for solving boundary value problems associated with the Lane-Emden equation, which frequently arises in astrophysics and various nonlinear models. A major challenge in studying this equation…
This paper is dedicated to the problem of isolating and validating zeros of non-linear two point boundary value problems. We present a method for such purpose based on the Newton-Kantorovich Theorem to rigorously enclose isolated zeros of…
This work is devoted to the study of the existence and sign of Green's functions for first order linear problems with constant coefficients and initial (one point) conditions. We first prove a result on the existence of solutions of $n$-th…
Many special functions are solutions of first order linear systems $y_n'(x)=a_n(x)y_n(x)+d_n(x)y_{n-1}(x)$, $y_{n-1}'(x)=b_n(x)y_{n-1}(x)+e_{n}(x)y_n(x)$. We obtain bounds for the ratios $y_n(x)/y_{n-1}(x)$ and the logarithmic derivatives…