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On the solvability of nonlinear boundary value problems on time scales.

机译：时间尺度上非线性边值问题的可解性。

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In this manuscript we study boundary value problems on time scales. First we will examine weakly nonlinear boundary value problems of the form xDt= Atxt +ht+ef t,xt, t∈ a,bT subject to B1xa+B 2xb=0, and analyze problems at resonance; that is, problems where the homogeneous linear boundary value problem has a nontrivial solution space. We establish conditions for the existence of solutions and discuss the dependence of solutions on parameters.;Next we consider the existence and properties of solutions to nonlinear dynamic equations of the form xDt= Atxt +qt+ft,x t, t∈a,b T subject to global boundary conditions. Our most significant result in this section concerns the existence of solutions of problems where the nonlinearity exhibits sublinear growth.;Finally we establish sufficient conditions for the solvability of nonlinear scalar two-point boundary value problems at resonance. As a consequence of our results we are able to provide easily verifiable conditions for the existence of periodic behavior for dynamic equations on time scales.

机译：在这份手稿中，我们研究时标上的边值问题。首先，我们将研究受B1xa + B 2xb = 0约束的形式为xDt = Atxt + ht + ef t，xt，t∈a，bT的弱非线性边值问题，并分析共振时的问题；也就是说，齐次线性边界值问题具有非平凡的解空间的问题。我们为解的存在建立条件并讨论解对参数的依赖性。接下来，我们考虑形式为xDt = Atxt + qt + ft，xt，t∈a，b T的非线性动力学方程解的存在性和性质。受全球边界条件的约束。在本节中，我们最重要的结果涉及存在非线性表现出亚线性增长的问题的解决方案。最后，我们为谐振时非线性标量两点边值问题的可解性建立了充分条件。作为我们结果的结果，我们能够为时标上的动态方程的周期行为的存在提供容易验证的条件。

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作者
Kalhorn, Rebecca Isabel Burton.;
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作者单位

North Carolina State University.;

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授予单位 North Carolina State University.;
学科 Mathematics.
学位 Ph.D.
年度 2009
页码 73 p.
总页数 73
原文格式 PDF
正文语种 eng
中图分类数学;
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On the solvability of nonlinear boundary value problems on time scales.

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