Positive solutions for quasilinear second order differential equation |
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Authors: | Shijie Dong Weigao Ge |
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Affiliation: | 1. Department of Mathematics , Mechanical Engineering College , Shijiazhuang, 050003, P.R. China jie_ds@sina.com;3. Department of Applied Mathematics , Beijing Institute of Technology , Beijing, 100081, P.R. China |
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Abstract: | It is well known that the Krasnoselskii's fixed point theorem is very very important. It was extensively used for studying the boundary value problems. In this article, the Krasnoselskii's fixed point theorem is extended. The new fixed point theorem is obtained. The second order quasilinear differential equation (Φ (y′))′+a(t)f(t,y,y′)=0,, 0f is a nonnegative continuous function, Φ (v)= |v|p-2 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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Keywords: | Quasilinear differential equation Fixed point theorem in cone Positive solution 34B10 34B15 |
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