First, existence criteria for at least three nonnegative solutions to the following boundary value problem of fourth-order difference equation Δ4x(t− 2) = a(t) f (x(t)), t ∈ [2,T], x(0)= x(T +2)=0, Δ2x(0)=Δ2x(T)=0 are established by using the well-known LeggettWilliams fixed point theorem, and then, for arbitrary positive integerm, existence results for at least 2m− 1 nonnegative solutions are ...

where the sum is over all different solutions in nonnegative integers b1, . . . , bm of b1 + 2b2 + · · · + mbm = m, and k := b1 + · · · + bm. For example, when m = 3 this instructs us to look at all solutions in nonnegative integers of the equation b1 + 2b2 + 3b3 = 3. We can have b3 = 1, b1 = 0 = b2, in which case k = 1 and we get the term 3! 0! 0! 1! ′ ( f (t)) ( f ′′′(t) 3! ) = g′ ( f (t)) f ...

Nonnegative and compartmental dynamical system models are widespread in biological, physiological, and pharmacological sciences. Since the state variables of these systems are typically masses or concentrations of a physical process, it is of interest to determine necessary and sufficient conditions under which the system states possess monotonic solutions. In this paper, we present necessary a...

In this paper, we study the multiplicity of nontrivial nonnegative solutions for a semilinear elliptic equation involving nonlinear boundary condition and sign-changing potential. With the help of the Nehari manifold, we prove that the semilinear elliptic equation: −∆u+ u = λf(x)|u|q−2u in Ω, ∂u ∂ν = g(x)|u|p−2u on ∂Ω, has at least two nontrivial nonnegative solutions for λ is sufficiently small.

We consider dimension reduction for solutions of the Kähler-Ricci flow with nonegative bisectional curvature. When the complex dimension n = 2, we prove an optimal dimension reduction theorem for complete translating KählerRicci solitons with nonnegative bisectional curvature. We also prove a general dimension reduction theorem for complete ancient solutions of the Kähler-Ricci flow with nonneg...

This paper deals with a p-Kirchhoff type problem involving signchanging weight functions. It is shown that under certain conditions, by means of variational methods, the existence of multiple nontrivial nonnegative solutions for the problem with the subcritical exponent are obtained. Moreover, in the case of critical exponent, we establish the existence of the solutions and prove that the ellip...

We investigate the existence and the nature of the solutions of the matrix equation Ax = b, where A is a Z-matrix and b is a nonnegative vector. When x is required to be nonnegative, then an existence theorem is due to Carlson and Victory and is re-proved in this paper. We apply our results to study nonnegative vectors in the range of Z-matrices.

We consider a semilinear elliptic equation on a smooth bounded domain Ω in R2, assuming that both the domain and the equation are invariant under reflections about one of the coordinate axes, say the y-axis. It is known that nonnegative solutions of the Dirichlet problem for such equations are symmetric about the axis, and, if strictly positive, they are also decreasing in x for x > 0. Our goal...