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Traveling wave solutions in a class of higher dimensional lattice differential systems with delays and applications

Yanli He, Kun Li (2021)

Applications of Mathematics

In this paper, we are concerned with the existence of traveling waves in a class of delayed higher dimensional lattice differential systems with competitive interactions. Due to the lack of quasimonotonicity for reaction terms, we use the cross iterative and Schauder's fixed-point theorem to prove the existence of traveling wave solutions. We apply our results to delayed higher-dimensional lattice reaction-diffusion competitive system.

Unboundedness results for systems

Gabriel Lugo, Frank Palladino (2009)

Open Mathematics

We study k th order systems of two rational difference equations x n = α + ∑ i = 1 k β i x n - i + ∑ i = 1 k γ i y n - i A + ∑ j = 1 k B j x n - j + ∑ j = 1 k C j y n - j , n ∈ ℕ , In particular we assume non-negative parameters and non-negative initial conditions. We develop several approaches which allow us to prove that unbounded solutions exist for certain initial conditions in a range of the parameters.

Value distribution of meromorphic solutions of homogeneous and non-homogeneous complex linear differential-difference equations

Li-Qin Luo, Xiu-Min Zheng (2016)

Open Mathematics

In this paper, we investigate the value distribution of meromorphic solutions of homogeneous and non-homogeneous complex linear differential-difference equations, and obtain the results on the relations between the order of the solutions and the convergence exponents of the zeros, poles, a-points and small function value points of the solutions, which show the relations in the case of non-homogeneous equations are sharper than the ones in the case of homogeneous equations.

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