A Nonlocal Free Boundary Problem

Homogenization of a nonlocal elastohydrodynamic lubrication problem: a new free boundary model

Spherical Solutions to a Nonlocal Free Boundary Problem from Diblock Copolymer Morphology

The Γ-limit of the Ohta-Kawasaki density functional theory of diblock copolymers is a nonlocal free boundary problem. For some values of block composition and the nonlocal interaction, an equilibrium pattern of many spheres exists in a three dimensional domain. A sub-range of the parameters is found where the multiple sphere pattern is stable. This stable pattern models the spherical phase in t...

A Nonlinear Second Order Problem Witha Nonlocal Boundary Condition

We study a nonlinear problem of pendulum-type for a p-Laplacian with nonlinear periodic-type boundary conditions. Using an extension of Mawhin’s continuation theorem for nonlinear operators, we prove the existence of a solution under a LandesmanLazer type condition. Moreover, using the method of upper and lower solutions, we generalize a celebrated result by Castro for the classical pendulum eq...

A Third Order Nonlocal Boundary Value Problem at Resonance

We consider the third-order nonlocal boundary value problem u ′′′ (t) = f (t, u(t)), a.e. in (0, 1), u(0) = 0, u ′ (ρ) = 0, u ′′ (1) = λ[u ′′ ], where 0 < ρ < 1, the nonlinear term f satisfies Carathéodory conditions with respect to L 1 [0, T ], λ[v] = 1 0 v(t) dΛ(t), and the functional λ satisfies the resonance condition λ[1] = 1. The existence of a solution is established via Mawhin's coincid...

Ground State Solution of a Nonlocal Boundary-value Problem

In this article, we apply the Nehari manifold method to study the Kirchhoff type equation