Singular second order boundary value problems
Nonlinear Analysis: Theory, Methods & Applications
A generalized Emden-Fowler equation with a negative exponent
Nonlinear Analysis: Theory, Methods & Applications
The existence of positive solutions of nonlinear singular second-order boundary value problems
Mathematical and Computer Modelling: An International Journal
Positive solutions to singular initial value problems with sign changing nonlinearities
Mathematical and Computer Modelling: An International Journal
Journal of Computational and Applied Mathematics
| Hi-index | 7.29 |
Consider the nonlinear scalar differential equations 1/p(t) (p(t)y'(t))' + sign(1 - α)q(t)f(t, y(t), p(t)y'(t)) = 0, where α 0, α ≠ 1, p and q are "singular" at t=0, 1 and f ∈ C((0, 1) × R+ × R-, R-), associated to boundary conditions γy(0) + δlimt →0+ p(t)y'(t) = 0, γ 0, limt →1- p(t)y'(t)= α limt →0+ p(t)y'(t). Existence of a monotone positive solutions of this BVP are given, with their slope a priori bounded, under superlinear or sublinear growth in f. The approach is based on the analysis of the corresponding vector field on the face-plane and the well-known shooting technique.