A Nonlinear Inequality Arising in Geometry and Calabi-Bernstein Type Problems

A Nonlinear Inequality Arising in Geometry and Calabi-Bernstein Type Problems

New examples of Calabi–Bernstein problems for some nonlinear equations

All the entire solutions to the maximal surface equation in certain 3-dimensional Lorentzian manifolds, obeying the null energy condition, are obtained. Thus, we solve new Calabi–Bernstein problems. As a consequence, the corresponding parametric versions are also given. The behaviour of this Calabi– Bernstein property with respect to an special family of C2-perturbations of Lorentz–Minkowski sp...

A Nonlinear Inequality and Evolution Problems

Assume that g(t) ≥ 0, and ġ(t) ≤ −γ(t)g(t) + α(t, g(t)) + β(t), t ≥ 0; g(0) = g0; ġ := dg dt , on any interval [0, T ) on which g exists and has bounded derivative from the right, ġ(t) := lims→+0 g(t+s)−g(t) s . It is assumed that γ(t), and β(t) are nonnegative continuous functions of t defined on R+ := [0,∞), the function α(t, g) is defined for all t ∈ R+, locally Lipschitz with respect to g u...

a cauchy-schwarz type inequality for fuzzy integrals

نامساوی کوشی-شوارتز در حالت کلاسیک در فضای اندازه فازی برقرار نمی باشد اما با اعمال شرط هایی در مسئله مانند یکنوا بودن توابع و قرار گرفتن در بازه صفر ویک می توان دو نوع نامساوی کوشی-شوارتز را در فضای اندازه فازی اثبات نمود.

A Sharp Bernstein-type Inequality for Exponential Sums

A subtle Bernstein-type extremal problem is solved by establishing the equality sup 06=f∈e E2n |f ′(0)| ‖f‖[−1,1] = 2n − 1 , where e E2n := ( f : f(t) = a0 + n X j=1 aje λjt + bje −λjt , aj , bj , λj ∈ R ) . This settles a conjecture of Lorentz and others and it is surprising to be able to provide a sharp solution. It follows fairly simply from the above that 1 e − 1 n − 1 min{y − a, b − y} ≤ s...