A Necessary and Sufficient Condition for Pseudo-symmetric Positive Solutions of Boundary Value Problems
نویسنده
چکیده
Recently, many authors have focused on the question of symmetric positive solutions for ordinary differential equation boundary value problems, for example, see (Avery & Henderson, 2000; Çetin & Topal, 2012; Graef & Kong, 2008; Hamal & Yoruk, 2010; Jiang, Liu & Wu, 2013; Luo & Luo, 2010; Luo & Luo, 2012; Lin & Zhao, 2013; Tersenov, 2014) and the references therein. In (Avery & Henderson, 2003), Avery and Henderson gave the definition of pseudo-symmetric function. Since then, some papers have discussed the pseudo-symmetric question and established sufficient conditions for the existence of pseudo-symmetric positive solutions, see (Feng, Zhang & Ge, 2010; Guo, Han & Chen, 2010; Ji, 2008; Ma & Ge, 2007; Pang, 2009; Sun & Zhao, 2014 ). To the best of the authors’ knowledge there is little known about necessary and sufficient conditions for second-order pseudosymmetric nonlinear boundary value problem. Motivated by the works mentioned above, we aim to establish a necessary and sufficient condition for the existence of pseudo-symmetric positive solution of (1.1) by applying the monotone iterative technique.
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