• The Pure and Applied Mathematics
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• v.4 no.2
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• pp.161-166
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• 1997

We obtained sufficient conditions for $\phi$(t)-stability and uniform $\phi$(t)-stability of the trivial solution of comparison differential system. we also investigated the corresponding stability concepts of the trivial solution of the differential system using the thoery of differential inequlities through cones and the method of conevalued Lyapunov functions.

• The Pure and Applied Mathematics
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• v.15 no.4
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• pp.407-414
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• 2008

In this paper, we study the self-adjoint second order boundary value problem with integral boundary conditions: (p(t)x'(t))'+f(t,x(t))=0, t $${\in}$$ (0,1), x'(0)=0, x(1) = $${\int}_0^1$$ x(s)g(s)ds. A new result on the existence of positive solutions is obtained. The interesting points are: the first, we employ a new tool-the recent Leggett-Williams norm-type theorem for coincidences; the second, the boundary value problem is involved in integral condition; the third, the solutions obtained are positive.