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Nonlinear superlinear singular and nonsingular second order boundary value problems. (English) Zbl 0902.34015

In the study of nonlinear phenomena many mathematical models give rise to the differential equation

1 p(py ' ) ' +qf(t,y,py ' )=0,0<t<1(1)

subject to the boundary conditions

lim t0 + p(t)y ' (t)=y(1)=0(3)

with pC[0,1]C 1 (0,1) and p>0 on (0,1), qC(0,1) with q>0 on (0,1) and

0 1 p(x)q(x)dx<, 0 1 1 p(s) 0 s p(x)q(x)dxds<,

and f:[0,1]×(0,)×(-,0] is continuous.

The authors prove the existence of a solution y(t)C[0,1]C 2 (0,1) with y>0 on (0,1) to the problems (1), (2) and (1), (3) if there are some supplementary assumptions on p(t), q(t), and f(t,y,z).

34B15Nonlinear boundary value problems for ODE