A. Lomtatidze, Mathematical Institute of the Academy of Sciences of the Czech Republic, Zizkova 22, 616 62 Brno, Czech Republic, and Department of Mathematical Analysis, Faculty of Natural Sciences, Masaryk University, Janackovo nam. 2a, 662 95 Brno, Czech Republic, e-mail: bacho@math.muni.cz; P. Torres, Departamento de Matematica Aplicada, Universidad de Granada, 18071 Granada, Spain, e-mail: ptorres@ugr.es
Abstract: The problem on the existence of a positive in the interval $\mathopen]a,b\mathclose[$ solution of the boundary value problem
u"=f(t,u)+g(t,u)u';\quad u(a+)=0, \quad u(b-)=0
is considered, where the functions $f$ and $g \mathopen]a,b\mathclose[\times\mathopen]0,+\infty\mathclose[ \to\bb R$ satisfy the local Caratheodory conditions. The possibility for the functions $f$ and $g$ to have singularities in the first argument (for $t=a$ and $t=b$) and in the phase variable (for $u=0$) is not excluded. Sufficient and, in some cases, necessary and sufficient conditions for the solvability of that problem are established.
Keywords: second order singular equation, two-point boundary value problem, solvability
Classification (MSC 2000): 34B10, 34B18
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