We establish the existence/nonexistence and multiplicity of nontrivial nonnegative solutions for the following 0-Dirichlet problem with mean curvature operator in the Minkowski space  −div ( ∇u √ 1−|∇u|2 ) = λf(x, u) in Ω, u = 0 on ∂Ω, where Ω is a general bounded domain of RN . By bifurcation and topological methods, we determine the interval of parameter λ in which the above problem has zer...

Hocherman and Rosenau conjectured that long-wave unstable Cahn-Hilliard-type interface models develop finite-time singularities when the nonlinearity in the destabilizing term grows faster at large amplitudes than the nonlinearity in the stabilizing term (Phys. D 67, 1993, pp. 113–125). We consider this conjecture for a class of equations, often used to model thin films in a lubrication context...

We study the existence of multiple nonnegative solutions for the doubly singular threepoint boundary value problem with derivative dependent data function − p t y′ t ′ q t f t, y t , p t y′ t , 0 < t < 1, y 0 0, y 1 α1y η . Here, p ∈ C 0, 1 ∩ C1 0, 1 with p t > 0 on 0, 1 and q t is allowed to be discontinuous at t 0. The fixed point theory in a cone is applied to achieve new and more general re...

A scaling of a nonnegative matrix A is a matrix XA Y -I. where X and Yare nonsingular. nonnegative diagonal matrices. Some condition may be imposed on the scaling, for exa'mple. when A is square, X = Y or det X = det Y. We characterize matrices for ' which there exists a scaling that satisfies predetermined upper and lower bound. Our principal tools are a piecewise linear theorem of the alterna...