Geodesic
POSITIVE SOLUTIONS OF NONLOCAL SINGULAR BOUNDARY VALUE PROBLEMS
Glasgow mathematical journal, Tome 46 (2004) no. 3, pp. 537-550

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DOI

The paper presents the existence result for positive solutions of the differential equation $(g(x))''=f(t,x,(g(x))')$ satisfying the nonlocal boundary conditions $x(0)=x(T)$, $\min\{ x(t): t \in J\}=0$. Here the positive function $f$ satisfies local Carathéodory conditions on $[0,T] \times (0,\infty) \times (\R {\setminus} \{0\})$ and $f$ may be singular at the value 0 of both its phase variables. Existence results are proved by Leray-Schauder degree theory and Vitali's convergence theorem.
DOI : 10.1017/S0017089504001983
Mots-clés : 34B16, 34B15 
AGARWAL, RAVI P.; O'REGAN, DONAL; STANĚK, SVATOSLAV. POSITIVE SOLUTIONS OF NONLOCAL SINGULAR BOUNDARY VALUE PROBLEMS. Glasgow mathematical journal, Tome 46 (2004) no. 3, pp. 537-550. doi: 10.1017/S0017089504001983
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     title = {POSITIVE {SOLUTIONS} {OF} {NONLOCAL} {SINGULAR} {BOUNDARY} {VALUE} {PROBLEMS}},
     journal = {Glasgow mathematical journal},
     pages = {537--550},
     year = {2004},
     volume = {46},
     number = {3},
     doi = {10.1017/S0017089504001983},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089504001983/}
}
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