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Zbl 0790.34027
Zhang, Yong
Existence of solutions of a kind of singular boundary value problem. (English)
[J] Nonlinear Anal., Theory Methods Appl. 21, No.2, 153-159 (1993). ISSN 0362-546X

The paper deals with solvability of the singular boundary value problem (BVP) ${1 \over q(t)} (p(t)u')'=f(t,u,pu')$, $t \in (0,1)$, $u(t)$ continuous at $t=0$, $u(1)=0$, where $p,q \in C[0,1]$, $p,q>0$ on (0,1] and $p(0)=0$, i.e., singularity is at $t=0$. It is also supposed that $\int\sp 1\sb 0p\sp{-1}(t)dt=\infty$ since if this integral is convergent, the considered BVP can be transformed into a regular one. The conditions imposed on the nonlinearity $f$ are weaker than similar conditions given by {\it D. R. Dunninger} and {\it J. C. Kurtz} [J. Math. Anal. Appl. 115, 369-405 (1986; Zbl 0616.34012)]. The principal method used in the proof of the main statement is the method of upper and lower solutions.
[O.Došlý (Brno)]

MSC 2000:: *34B15 Nonlinear boundary value problems of ODE
34E15 Asymptotic singular perturbations, general theory (ODE)

Keywords: singular boundary value problem; method of upper and lower solutions

Citations: Zbl 0616.34012

Cited in: Zbl 0853.34028 Zbl 0823.34031

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