【摘要】：本文主要應(yīng)用變分法研究了幾類二階離散Hamilton系統(tǒng)同宿軌的存在性和多重性,在現(xiàn)有結(jié)果的基礎(chǔ)上減弱非線性項(xiàng)的控制條件后得到相應(yīng)的結(jié)論,推廣和改進(jìn)了已有的工作.我們通過構(gòu)造變分結(jié)構(gòu)與工作空間,尋求系統(tǒng)所對(duì)應(yīng)泛函的近似臨界點(diǎn)序列,進(jìn)而證明系統(tǒng)解的存在性與多重性.全文大致可以分為三個(gè)部分,分別為：第一部分：介紹了問題產(chǎn)生的背景、研究現(xiàn)狀以及臨界點(diǎn)理論中的一些比較重要的基本知識(shí).第二部分：研究超二次二階離散Hamilton系統(tǒng)在L(t)不是全局正定,b(t)變號(hào),并且V(u(t))關(guān)于u是超二次的情況下,應(yīng)用臨界點(diǎn)理論中的山路定理得到了系統(tǒng)同宿軌的存在性與多重性.第三部分：研究次二次二階離散Hamilton系統(tǒng)是次二次的情況下,利用極小作用原理,在新的假設(shè)和新的條件下應(yīng)用臨界點(diǎn)理論得到了同宿軌的存在性.
[Abstract]:In this paper, the existence and multiplicity of homoclinic orbits for several second order discrete Hamilton systems are studied by using variational method. Based on the existing results, the control conditions of nonlinear terms are weakened and the corresponding conclusions are obtained, which generalize and improve the existing work. By constructing the variational structure and workspace, we seek the approximate critical point sequence of the functional corresponding to the system, and prove the existence and multiplicity of the solution of the system. The whole paper can be divided into three parts: the first part introduces the background of the problem, the present situation of the research and some important basic knowledge in the critical point theory. In the second part, we study the super-quadratic discrete Hamilton system under the condition that L (t) is not a global positive definite, b (t) sign and V (u (t) is super quadratic. The existence and multiplicity of homoclinic orbits are obtained by using the mountain path theorem in the critical point theory. In the third part, we study the existence of homoclinic orbits under new assumptions and new conditions by applying the critical point theory to the case that the second order discrete Hamilton system is of the second quadratic order, using the minimal action principle.
【學(xué)位授予單位】：華僑大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2016
【分類號(hào)】：O175
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本文編號(hào)：2318348