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Open Access Research

Existence and multiplicity of positive solutions for one-dimensional prescribed mean curvature equations

Yanqiong Lu, Ruyun Ma* and Hongliang Gao

Author Affiliations

Department of Mathematics, Northwest Normal University, Lanzhou, 730070, P.R. China

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Boundary Value Problems 2014, 2014:120  doi:10.1186/1687-2770-2014-120


Dedicated to Professor Ivan T. Kiguradze for his merits in the theory of differential equations

Published: 16 May 2014

Abstract

In this work, we establish the existence and multiplicity results of positive solutions for one-dimensional prescribed mean curvature equations. Our approach is based on fixed point index theory for completely continuous operators which leave invariant a suitable cone in a Banach space of continuous functions.

MSC: 34B10, 34B18.

Keywords:
mean curvature equations; positive solutions; existence; fixed point index