Positive solutions of singular positone dirichlet boundary value problems

Positive Solutions of a Singular Positone and Semipositone Boundary Value Problems for Fourth-Order Difference Equations

This paper studies the boundary value problems for the fourth-order nonlinear singular difference equationsΔ4u i−2 λα i f i, u i , i ∈ 2, T 2 , u 0 u 1 0, u T 3 u T 4 0. We show the existence of positive solutions for positone and semipositone type. The nonlinear term may be singular. Two examples are also given to illustrate the main results. The arguments are based upon fixed point theorems i...

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...

Positive Solutions for a Class of Singular Boundary-value Problems

This paper concerns the existence and multiplicity of positive solutions for Sturm-Liouville boundary-value problems. We use fixed point theorems and the sub-super solutions method to two solutions to the problem studied. Introduction Consider the boundary-value problem Lu = λf(t, u), 0 < t < 1 αu(0)− βu′(0) = 0, γu(1) + δu′(1) = 0, (0.1) where Lu = −(ru′)′ + qu, r, q ∈ C[0, 1] with r > 0, q ≥ ...

Positive Solutions of Singular Complementary Lidstone Boundary Value Problems

Positive Solutions for a Class of Singular Boundary-value Problems

Using regularization and the sub-super solutions method, this note shows the existence of positive solutions for singular differential equation subject to four-point boundary conditions.