We study a class of initial value problems for two-dimensional nonlinear wave equations. A new topological approach is applied to prove the existence at least two nonnegative classical solutions. The arguments are based upon recent theoretical result.

In this paper, we prove the existence of nontrivial nonnegative time periodic solutions for a pseudo-parabolic type equation with weakly nonlinear periodic sources. Moreover, we investigate the asymptotic behavior of solutions as the viscous coefficient k tends to zero.

In [LY] a differential Harnack inequality was proved for solutions to the heat equation on a Riemannian manifold. Inspired by this result, Hamilton first proved trace and matrix Harnack inequalities for the Ricci flow on compact surfaces [H0] and then vastly generalized his own result to all higher dimensions for complete solutions of the Ricci flow with nonnegative curvature operator [ H2]. So...

In this note, we present some Liouville type theorems about the nonnegative solutions to some indefinite elliptic equations.

The nonnegative matrix factorization (NMF) problem D = XY T for a given nonnegative matrix D and with nonnegative factors X and Y can have many solutions aside from trivial permutations or positive multiples of the columns of X and Y . The set of feasible solutions (SFS) is a low-dimensional representation of all possible columns of either X or Y in any NMF of D. The SFS provides important info...

in this paper, at rst for a given set of real or complex numbers  with nonnegative summation, we introduce some special conditions that with them there is no nonnegative tridiagonal matrix in which  is its spectrum. in continue we present some conditions for existence such nonnegative tridiagonal matrices.

In this paper, we investigate the local and global stability and the period two solutions of all nonnegative solutions of the difference equation, xn+1 = axn + bxn−k A + Bxn−k where a, b, A, B are all positive real numbers, k ≥ 1 is a positive integer, and the initial conditions x−k, x−k+1, ..., x0 are nonnegative real numbers. It is shown that the zero equilibrium point is globally asymptotica...