拟线性椭圆型问题解的定性分析
发布时间：2018-08-17 14:13
【摘要】：本文主要研究了几类拟线性椭圆型问题解的相关性质,具体包括解的存在性、非存在性以及多解性等.第一章研究拟线性椭圆型方程组正解的存在性与非存在性,其中Ω (?) RN为有界光滑区域或者Ω=RN(当上下解方法,我们得到当Ω为有界光滑区域或者Q=RN时,该问题至少存在一个正解,且当Ω=RN时,该问题不存在径向对称的有界正解.第二章研究一类含凹凸项和临界项的p-q-拉普拉斯方程组数人*0使得当λp/(p-r)+p/(μp-r)∈(0,∧*)时,该问题至少存在cat(Ω)+1个不同的正解,从而建立了方程组解的个数与区域拓扑之间的关系.第三章研究一类带有非线性边界条件的非齐次拟线性椭圆型方程组路引理和Ekeland变分准则,我们得到存在常数λ*,L0使得当入∈(0,λ*)时,该问题至少存在两个非平凡解,其中第四章研究一类含变号位势的p-Kirchhoff型方程组V∈C(RN,R)可变号,且函数F∈C1(RN×R2,R)满足一定的增长性条件.利用对称的山路引理,我们证得该问题存在无穷多个高能量的非平凡解.第五章在RN中研究一类具有临界指数增长的N-Kirchhoff型问题解的存在性与多解性,其中且函数f满足临界指数增长条件.结合变分法和RN中的Trudinger-Moser不等式,我们得到存在常数A0使得当λ∈(0,A)时,该问题至少存在两个正解.
[Abstract]:In this paper, we mainly study the related properties of solutions for quasilinear elliptic problems, including the existence, nonexistence and multiplicity of solutions. In chapter 1, we study the existence and nonexistence of positive solutions for quasilinear elliptic equations, where 惟 (?) RN is a bounded smooth region or 惟 -RN (when the upper and lower solution method, we obtain that if 惟 is a bounded smooth region or Q=RN, there is at least one positive solution to the problem, and if 惟 RN, the problem does not have a radial symmetric bounded positive solution. In chapter 2, we study a class of p-q-Laplacian equations with concave and convex terms and critical terms such that when 位 p / (p-r) p / (渭 p-r) 鈭，
本文编号：2187887
[Abstract]:In this paper, we mainly study the related properties of solutions for quasilinear elliptic problems, including the existence, nonexistence and multiplicity of solutions. In chapter 1, we study the existence and nonexistence of positive solutions for quasilinear elliptic equations, where 惟 (?) RN is a bounded smooth region or 惟 -RN (when the upper and lower solution method, we obtain that if 惟 is a bounded smooth region or Q=RN, there is at least one positive solution to the problem, and if 惟 RN, the problem does not have a radial symmetric bounded positive solution. In chapter 2, we study a class of p-q-Laplacian equations with concave and convex terms and critical terms such that when 位 p / (p-r) p / (渭 p-r) 鈭，
本文编号：2187887
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