Opuscula Math. 25, no. 2 (2005), 227-241
Opuscula Mathematica
A singular nonlinear boundary value problem with Neumann conditions
Abstract. We study the existence of solutions for the equations \(x^{\prime\prime}\pm g(t,x)=h(t)\), \(t\in (0,1)\) with Neumann boundary conditions, where \(g:[0,1] \times (0,+\infty) \to [0,+\infty)\) and \(h:[0,1] \to \mathbb{R}\) are continuous and \(g(t,\cdot)\) is singular at \(0\) for each \(t\in [0,1]\).
Keywords: singular nonlinear boundary value problem, Neumann boundary conditions, second order equations, maximal and minimal solutions.
Mathematics Subject Classification: 34K10.
- Julian Janus
- AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Cracow, Poland
- Received: 2004-11-10.
