Second order two-parametric quantum boundary value problems

IF 0.7 Q3 MATHEMATICS, APPLIED Differential Equations & Applications Pub Date : 2019-01-01 DOI:10.7153/dea-2019-11-10
Yousef Gholami
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引用次数: 1

Abstract

In this paper we study second order two-parametric quantum boundary value problems. The main aims of this paper are presented in two steps. In the first step, we consider second order two-parametric quantum boundary value problems with general nonlinearities and by the use of Krasnoselskii fixed point theorem on positive cones we provide some sufficient conditions to reach the existence, multiplicity and nonexistence of positive solutions. At the and of this step, some illustrative examples are given to show practical implementability of the obtained theoretical results. In the second step, we consider the corresponding two-parametric quantum eigenvalue problems and in the light of Lyapunov inequalities, we present a lower bound estimation for positive eigenvalues. We complete this step with a numerical evaluation to identify validity of the obtained lower bound.
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二阶双参数量子边值问题
本文研究了二阶双参数量子边值问题。本文的主要目的分为两个步骤。第一步,考虑具有一般非线性的二阶二参数量子边值问题,利用正锥上的Krasnoselskii不动点定理,给出了正解的存在性、多重性和不存在性的充分条件。在这一步的最后,给出了一些实例来说明所得到的理论结果的实际可实现性。第二步,我们考虑相应的双参数量子特征值问题,并根据Lyapunov不等式,给出了正特征值的下界估计。我们用数值评估来完成这一步,以确定所得到的下界的有效性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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