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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