Dead cores of singular Dirichlet boundary value problems with ϕ-Laplacian

Positive and dead core solutions of singular Dirichlet boundary value problems with phi-Laplacian

The paper discusses the existence of positive solutions, dead core solutions and pseudodead core solutions of the singular Dirichlet boundary value problem (φ(u)) = λ[ f (t, u, u) + h(t, u, u)], u(0) = u(T ) = A. Here λ is the positive parameter, A > 0, f is singular at the value 0 of its first phase variable and h may be singular at the value 0 of its second phase variable. c © 2007 Elsevier L...

Solvability for some boundary value problems with φ-Laplacian operators

We study the existence of solution for the one-dimensional φ-laplacian equation (φ(u′))′ = λf(t, u, u′) with Dirichlet or mixed boundary conditions. Under general conditions, an explicit estimate λ0 is given such that the problem possesses a solution for any |λ| < λ0.

Positive and Dead-Core Solutions of Two-Point Singular Boundary Value Problems with -Laplacian

Singular Dirichlet Problem for Ordinary Differential Equations with Φ-laplacian

We provide sufficient conditions for solvability of a singular Dirichlet boundary value problem with φ-Laplacian (φ(u)) = f(t, u, u), u(0) = A, u(T ) = B, where φ is an increasing homeomorphism, φ( ) = , φ(0) = 0, f satisfies the Carathéodory conditions on each set [a, b] × 2 with [a, b] ⊂ (0, T ) and f is not integrable on [0, T ] for some fixed values of its phase variables. We prove the exis...

Heteroclinic Solutions of Singular Φ−Laplacian Boundary Value Problems on Infinite Time Scales

In this paper, we derive sufficient conditions for the existence of heteroclinic solutions to the singular Φ-Laplacian boundary value problem, [ Φ(y(t)) ]∆ = f(t, y(t), y(t)), t ∈ T y(−∞) = −1, y(+∞) = +1, on infinite time scales by using the Brouwer invariance domain theorem. As an application we demonstrate our result with an example.