Superlinear Singular Problems on the Half Line

On existence of positive solutions of coupled integral boundary value problems for a nonlinear singular superlinear differential system

By constructing a special cone and using fixed point index theory, this paper investigates the existence of positive solutions of singular superlinear coupled integral boundary value problems for differential systems

An Existence Result of Positive Solutions for Singular Superlinear Boundary Value Problems and Its Applications

An Approximation Approach to Eigenvalue Intervals for Singular Boundary Value Problems with Sign Changing and Superlinear Nonlinearities

Recommended by Ivan T. Kiguradze This paper studies the eigenvalue interval for the singular boundary value problem −u gt, u λht, u, t ∈ 0, 1, u0 0 u1, where g h may be singular at u 0, t 0, 1, and may change sign and be superlinear at u ∞. The approach is based on an approximation method together with the theory of upper and lower solutions. Copyright q 2009 Haishen L ¨ u et al. This is an ope...

On the Behavior of Damped Quasi-Newton Methods for Unconstrained Optimization

We consider a family of damped quasi-Newton methods for solving unconstrained optimization problems. This family resembles that of Broyden with line searches, except that the change in gradients is replaced by a certain hybrid vector before updating the current Hessian approximation. This damped technique modifies the Hessian approximations so that they are maintained sufficiently positive defi...

Positive Solutions of Singular Fourth-order Boundary-value Problems

In this paper, we present necessary and sufficient conditions for the existence of positive C3[0, 1]∩C4(0, 1) solutions for the singular boundaryvalue problem x′′′′(t) = p(t)f(x(t)), t ∈ (0, 1); x(0) = x(1) = x′(0) = x′(1) = 0, where f(x) is either superlinear or sublinear, p : (0, 1) → [0,+∞) may be singular at both ends t = 0 and t = 1. For this goal, we use fixed-point index results.