本文選題：無(wú)窮區(qū)間邊值問(wèn)題 + 不動(dòng)點(diǎn)定理��； 參考：《廣州大學(xué)》2017年碩士論文

【摘要】：本文主要利用Guo-Krasnosel'skii不動(dòng)點(diǎn)定理、上下解方法、拓?fù)涠壤碚摵筒粍?dòng)點(diǎn)指數(shù)理論,研究無(wú)窮區(qū)間上邊值問(wèn)題解的存在性與多解性.第一章為緒論,簡(jiǎn)單介紹有關(guān)無(wú)窮區(qū)間上邊值問(wèn)題的相關(guān)背景和研究現(xiàn)狀,以及本文的主要研究?jī)?nèi)容.第二章主要討論如下無(wú)窮區(qū)間上的邊值問(wèn)題其中,k為正常數(shù),f ∈C([0,∞)) ×[[0,∞),[[0,∞)).在合適的空間上,利用Guoo Krasnosel'skii不動(dòng)點(diǎn)定理,得到了至少一個(gè)正解的存在性.此外,也將討論如下非線性項(xiàng)含有解導(dǎo)數(shù)的邊值問(wèn)題同樣利用Guo-Krasnosel'skii不動(dòng)點(diǎn)定理,并結(jié)合Green函數(shù)的性質(zhì),在合適的條件下建立了正解的存在性結(jié)果.第三章主要討論第二章中非線性項(xiàng)不含解導(dǎo)數(shù)的無(wú)窮區(qū)間上邊值問(wèn)題的多解性.在一定條件下,利用上下解方法和拓?fù)涠壤碚摻⒘酥辽偃齻�(gè)解的存在性結(jié)果.第四章,我們研究如下含參數(shù)邊值問(wèn)題其中,λ為正參數(shù),h, g ∈ C([0, ∞),(0, ∞)).在合適的條件下,利用上下解方法和不動(dòng)點(diǎn)指數(shù)理論,建立了無(wú)窮區(qū)間上含參數(shù)邊值問(wèn)題的全局性結(jié)果,即正解的存在性、不存在性以及多解性.
[Abstract]:Using Guo-Krasnoselskii fixed point theorem, upper and lower solution methods, topological degree theory and fixed point exponent theory, the existence and multiplicity of solutions for boundary value problems over infinite intervals are studied in this paper. The first chapter is an introduction, which briefly introduces the background and research status of boundary value problems over infinite intervals, and the main research contents of this paper. In chapter 2, we mainly discuss the boundary value problem on infinite interval, where k is a normal number f 鈭，

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