Abstract
It is well known that Krasnose'skii fixed point theorem is very important. It was extensively used for studying the boundary value problems. In this paper, Krasnose'skii fixed point theorem is extended. A new fixed point theorem is obtained. The second order quasilinear differential equation (Phi(y'))' + a(t)f(t,y,y') = 0, 0 < t < 1 subject to Dirichlet boundary condition is studied, where f is a non-negative continuous function, Phi(v) = |v| <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p-2</sup> v, p > 1. We show the existence of at least one positive solution by using the new fixed point theorem in cone.
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