The existence of positive solutions for the singular two-point boundary value problem

Yanmin Niu, Baoqiang Yan

DOI: http://dx.doi.org/10.12775/TMNA.2017.004

Abstract


In this paper, we consider the following boundary value problem: $$ \begin{cases} ((-u'(t))^n)'=nt^{n-1}f(u(t)) &\text{for }0< t< 1,\\ u'(0)=0,\quad u(1)=0, \end{cases} $$% where $n> 1$. Using the fixed point theory on a cone and approximation technique, we obtain the existence of positive solutions in which $f$ may be singular at $u=0$ or $f$ may be sign-changing.

Keywords


Singular differential equation; two-point boundary value problem; fixed point theorem; positive solution

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