Opuscula Math. 25, no. 2 (2005), 227-241

Opuscula Mathematica

A singular nonlinear boundary value problem with Neumann conditions

Julian Janus

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.

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  • Julian Janus
  • AGH University of Science and Technology, Faculty of Applied Mathematics, al. Mickiewicza 30, 30-059 Cracow, Poland
  • Received: 2004-11-10.
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Julian Janus, A singular nonlinear boundary value problem with Neumann conditions, Opuscula Math. 25, no. 2 (2005), 227-241

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