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This paper is concerned with a class of nonlinear difference inequalities which include many different classes of difference inequalities and equations as special cases. By means of a Riccati type transformation, necessary and sufficient conditions for the existence of eventually positive solutions and positive nonincreasing solutions are obtained. Various type of comparison theorems are also derived as applications, which extends many theorems in the literature.

Existence for a class of discrete hyperbolic problems.

Luca, Rodica (2006)

Advances in Difference Equations [electronic only]

Existence, multiplicity and infinite solvability of positive solutions for $p$ -Laplacian dynamic equations on time scales.

Wang, Da-Bin (2006)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence of a positive solution for an $n$ th order boundary value problem for nonlinear difference equations.

Henderson, Johnny, Lauer, Susan D. (1997)

Abstract and Applied Analysis

Existence of a positive solution to a nonlocal semipositone boundary value problem on a time scale

Christopher S. Goodrich (2013)

Commentationes Mathematicae Universitatis Carolinae

We consider the existence of at least one positive solution to the dynamic boundary value problem $\begin{matrix} - y^{Δ Δ} (t) & = λ f (t, y (t)), t \in {[0, T]}_{𝕋} y (0) & = \int_{τ_{1}}^{τ_{2}} F_{1} (s, y (s)) Δ s y (σ^{2} (T)) & = \int_{τ_{3}}^{τ_{4}} F_{2} (s, y (s)) Δ s, \end{matrix}$ where $𝕋$ is an arbitrary time scale with $0 < τ_{1} < τ_{2} < σ^{2} (T)$ and $0 < τ_{3} < τ_{4} < σ^{2} (T)$ satisfying $τ_{1}$ , $τ_{2}$ , $τ_{3}$ , $τ_{4} \in 𝕋$ , and where the boundary conditions at $t = 0$ and $t = σ^{2} (T)$ can be both nonlinear and nonlocal. This extends some recent results on second-order semipositone dynamic boundary value problems, and we illustrate these extensions with some examples.

Existence of countably many positive solutions for $n$ th-order $m$ -point boundary-value problems on time scales.

Liang, Sihua, Zhang, Jihui, Wang, Zhiyong (2008)

Electronic Journal of Differential Equations (EJDE) [electronic only]

Existence of different kind of solutions for discrete time equations

Denis Pennequin (2014)

Nonautonomous Dynamical Systems

The aim of this paper is to extend the classical linear condition concerning diagonal dominant bloc matrix to fully nonlinear equations. Even if assumptions are strong, we obtain an explicit condition which exactly extend the one known in linear case, and the setting allows also to consider bicontinuous operator instead of the schift and as particular case, we receive periodic or almost periodic solutions for discrete time equations.

Existence of differentiable solutions of a system of functional equations of first order

Z. Krzeszowiak-Dybiec (1980)

Annales Polonici Mathematici

Existence of entire solutions of nonlinear difference equations

Kai Liu, Lianzhong Yang, Xinling Liu (2011)

Czechoslovak Mathematical Journal

In this paper we obtain that there are no transcendental entire solutions with finite order of some nonlinear difference equations of different forms.

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Displaying 61 – 80 of 137

Existence and uniqueness of nontrivial solutions for nonlinear higher-order three-point eigenvalue problems on time scales.

Existence and uniqueness of positive solution for singular BVPs on time scales.

Existence and uniqueness of solutions of higher-order antiperiodic dynamic equations.

Existence and uniqueness of solutions of non-linear functional equations of r-th order

Existence and uniqueness of the analytic solution of a nonlinear functional equation. (Russisch).

Existence criteria and classification schemes for positive solutions of second-order nonlinear difference systems.

Existence criteria for positive solutions of a nonlinear difference inequality

Existence for a class of discrete hyperbolic problems.

Existence, multiplicity and infinite solvability of positive solutions for $p$ -Laplacian dynamic equations on time scales.

Existence of a positive solution for an $n$ th order boundary value problem for nonlinear difference equations.

Existence of a positive solution to a nonlocal semipositone boundary value problem on a time scale

Existence of countably many positive solutions for $n$ th-order $m$ -point boundary-value problems on time scales.

Existence of different kind of solutions for discrete time equations

Existence of differentiable solutions of a system of functional equations of first order

Existence of entire solutions of nonlinear difference equations

Existence of homoclinic orbit for second-order nonlinear difference equation.

Existence of homoclinic solutions for a class of nonlinear difference equations.

Existence of monotone solutions of a difference equation.

Existence of multiple positive solutions for discrete problems with $p$ -Laplacian via variational methods.

Existence of multiple solutions for a class of $n$ -dimensional discrete boundary value problems.

Currently displaying 61 – 80 of 137