發(fā)布時(shí)間：2018-08-27 13:40

【摘要】：Kirchhoff型方程是一種經(jīng)典的非局部問(wèn)題,近年來(lái)逐步引起人們的關(guān)注,相關(guān)研究日益深入。本文利用臨界點(diǎn)理論討論了兩類(lèi)帶有參數(shù)Kirchhoff型非線性橢圓方程解的存在性,其中一類(lèi)帶有Dirichlet邊界條件,而另一類(lèi)帶有非線性Neumann邊界條件。對(duì)于第一類(lèi)方程,主要利用變分原理研究了當(dāng)參數(shù)變化時(shí)其解的存在性和多重性,建立了三個(gè)存在性結(jié)果,同時(shí)還討論此類(lèi)方程正解的分歧現(xiàn)象。對(duì)于第二類(lèi)方程,主要利用Bonanno和Bisci變分原理研究其無(wú)窮多解的存在性,給出了保證存在無(wú)窮多解的若干條件。
[Abstract]:Kirchhoff equation is a kind of classical nonlocal problem, which has been paid more and more attention in recent years. In this paper, we discuss the existence of solutions for two classes of nonlinear elliptic equations with parameters Kirchhoff type by using the critical point theory, one with Dirichlet boundary conditions and the other with nonlinear Neumann boundary conditions. For the first kind of equations, the existence and multiplicity of the solutions are studied by means of variational principle, and three existence results are established. The bifurcation of positive solutions of this kind of equations is also discussed. For the second kind of equations, the existence of infinite solutions is studied by using Bonanno and Bisci variational principles, and some conditions are given to guarantee the existence of infinite solutions.
【學(xué)位授予單位】：湖南科技大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類(lèi)號(hào)】：O175

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本文編號(hào)：2207462