p-Laplacian论文带Hardy项的拟线性方程的正解性.docVIP

p-Laplacian论文：带Hardy项的拟线性方程的正解性 【中文摘要】本文讨论下面方程的可解性,其中Ω是RN中具有光滑边界 ? Ω的有界区域,Δpu div |▽u|p-2▽u 为p-Laplacian,1 p N,λ 0是一个参数,0≤μ N-p /p pμ,非线性项h:Ω×R→[0,∞ 是一个非负连续函数,且在原点附近为p-渐进线性增长,在无穷远处为p-超线性增长并满足其他一些适当的条件.本文利用变分技巧、上下解方法、山路引理和比较原理证明了在情况0 λ λ1,6和λ λ1,b下,问题 ρλ 至少存在一个正解；在λ λ1,b情况下,问题 ρλ 至少存在两个正解,其中λ1,b是非线性特征值问题关于某个权函数b x ∈L∞ Ω 的第一特征值.并且本文还讨论了最后所获得的解关于λ→0和λ→λ1,b+的渐近性态. 【英文摘要】In this thesis, we will be concerned with the existence of solutions for the following eqautions whereΩis a domain of RN with the smooth boundary ? Q,Δpu div |▽u|p-2▽u is the p-Laplacian, 1 p N,λ 0 is a parameter,0≤μ N-p /p p ? μ, the nonlinear term h:Ω×R→[0,∞ is a nonnegative function, h has a p-asymptotically linear growth near zero and has a p-superlinear growth at infinity, and h satifies some other conditions.In this thesis, by using the variational techniques, sub and super solution method, the mountain pass lemma and the comparison principle, we obtian that the equation Pλ has at least one positive solution under both cases of 0 λ λ1,b andλ λ1,b, and the equation Pa has at least two positive solutions in the case ofλ λ1,b, whereλ1,b is the first eigenvalue of the following eigenvalue problem for some weight function b x €L∞ Ω . Moreover we discuss the asymptotic behavior of the solution whenλ→0 andλ→λ1,b+. 【关键词】p-Laplacian 山路引理 上下解方法 比较原理 正解 【英文关键词】p-Laplacian mountain pass theorem sub and super solution method comparison principle positive solution 【备注】索购全文在线加好友：1.3.9.9.3.8848 同时提供论文写作一对一指导和论文发表委托服务 【目录】带Hardy项的拟线性方程的正解性 摘要 4-5 Abstract 5 引言 7-11 第一章 预备知识 11-19 §1.1 基本定义和引理 11-12 §1.2 两个引理及其证明 12-19 第二章 主要结果及证明 19-27 结论与问题展望 27-28 参考文献 28-32 致谢 32