Global Solutions to Nonlinear Two‐Phase Free Boundary Problems

Solutions of Nonlinear Singular Boundary Value Problems

We study the existence of solutions to a class of problems u + f(t, u) = 0, u(0) = u(1) = 0, where f(t, ·) is allowed to be singular at t = 0, t = 1.

Positive Solutions To Nonlinear Semipositone Boundary Value Problems

In this paper, we investigate the following third-order three-point semipositone boundary value problems: ( ) ( , ) 0, (0,1); (0) ( ) (1) 0, u t f t u t

Existence of Three Positive Solutions to Nonlinear Boundary Value Problems

Exact Boundary Behavior of Solutions to Singular Nonlinear Dirichlet Problems

In this article we analyze the exact boundary behavior of solutions to the singular nonlinear Dirichlet problem −∆u = b(x)g(u) + λa(x)f(u), u > 0, x ∈ Ω, u|∂Ω = 0, where Ω is a bounded domain with smooth boundary in RN , λ > 0, g ∈ C1((0,∞), (0,∞)), lims→0+ g(s) = ∞, b, a ∈ Cα loc(Ω), are positive, but may vanish or be singular on the boundary, and f ∈ C([0,∞), [0,∞)).

Boundary Regularity of Weak Solutions to Nonlinear Elliptic Obstacle Problems

for all v∈ ={v∈W 0 (Ω), v≥ψ a.e. in Ω}. Here Ω is a bounded domain in RN (N≥2) with Lipschitz boundary, 2≤ p ≤N . A(x,ξ) :Ω×RN → RN satisfies the following conditions: (i) A is a vector valued function, the mapping x → A(x,ξ) is measurable for all ξ ∈ RN , ξ → A(x,ξ) is continuous for a.e. x ∈Ω; (ii) the homogeneity condition: A(x, tξ)= t|t|p−2A(x,ξ), t ∈ R, t = 0; (iii) the monotone inequality...