本文選題：耦合系統(tǒng) + 差分方程　； 參考：《廣州大學(xué)》2017年碩士論文

【摘要】：本文主要研究了二階耦合差分系統(tǒng)邊值問題非平凡解的不存在性和存在性.首先,我們建立適當(dāng)?shù)淖兎址汉?將尋求耦合差分系統(tǒng)邊值問題非平凡解的存在性轉(zhuǎn)化為對(duì)應(yīng)泛函的臨界點(diǎn)的存在性.在系數(shù)滿足一定條件下,我們研究了耦合差分系統(tǒng)邊值問題非平凡解的不存在性,然后應(yīng)用臨界點(diǎn)定理,得到了相應(yīng)耦合差分系統(tǒng)邊值問題存在非平凡解的一系列充分條件.全文的結(jié)構(gòu)如下:第一章簡述了問題產(chǎn)生的歷史背景和研究意義,相關(guān)的預(yù)備知識(shí)以及已有結(jié)果和本文的主要工作.第二章在系數(shù)滿足一定條件下,研究了二階耦合差分系統(tǒng)邊值問題非平凡解的不存在性.第三章利用臨界點(diǎn)定理,研究了二階耦合差分系統(tǒng)邊值問題非平凡解的存在性.
[Abstract]:In this paper, the nonexistence and existence of nontrivial solutions of boundary value problems for second order coupled difference systems are studied. First of all, we establish appropriate variational functional and transform the existence of nontrivial solution to the critical point of the corresponding functional from seeking the existence of nontrivial solution for the boundary value problem of coupled difference system to the existence of the critical point of the corresponding functional. In this paper, we study the nonexistence of nontrivial solutions for boundary value problems of coupled difference systems under certain conditions. Then, by applying the critical point theorem, we obtain a series of sufficient conditions for the existence of nontrivial solutions for boundary value problems of coupled difference systems. The structure of the thesis is as follows: in Chapter 1, the historical background and research significance of the problem are briefly introduced, the relevant preparatory knowledge, the existing results and the main work of this paper are also discussed. In chapter 2, we study the nonexistence of nontrivial solutions for boundary value problems of second order coupled difference systems under certain conditions. In chapter 3, by using the critical point theorem, we study the existence of nontrivial solutions for boundary value problems of second order coupled difference systems.
【學(xué)位授予單位】：廣州大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O175.7

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本文編號(hào)：2074079