Existence theorems for a class of two point boundary problems
Existence theorems for a class of two point boundary problems
复制标题
一类两点边界问题的存在定理
DOI：
10.1016/0022-0396(75)90043-1
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发表时间：
1975
影响因子：
2.4
通讯作者：
V. Barbu
中科院分区：
文献类型：
--
作者：
V. Barbu
本文研究Hilbert空间IT中的边值问题——d/dt (Fp (du/dt))+ Au (t) 3f (t), ae (E) O, t [, U-1) bww~(O)),-ww~~(w E% 40), 4w U-2)，其中a是从H到自身的极大单调算子（非线性），v（具体地说，I）是从H（具体地说，H x H）到[-co，+ CXJ]的下半连续凸函数。这里&I（具体来说是al）表示CZJ（具体来说是1）的子微分。需要强调的是，式（1.1）和式（1.2）作为特例包括了许多其他类型的非线性两点边界问题。例如如果z (u, 2 ~ ~) = 4 (4 + h (d th en边界条件(1.2)可以写熟悉的形式下aq +霍奇金淋巴瘤/ dt (o)) az, (u (o)) 3 0, aq@ u / dt (T)) +基地(T)) 3 0。(1.3)其他类型的边界条件为情商。(1.1)通过条件同时纳入问题z (u (o), u (T)) < +有限公司存在的主要结果,定理1,表示在第三节和第四节证明了凸分析和单调算子的方法。该结果可与作者[1]的结果以及BrCzis[4]和Pave1[1]的结果进行比较。在第5节中，通过椭圆正则化，我们利用这个结果得到了演化变分不等式的存在性定理
This paper deals with the boundary value problem--d/dt (Fp (du/dt))+ Au (t) 3f (t), ae t E] O, T [, U-1) bww~(O)),-ww~~(w E% 40), 4w U-2) in a Hilbert space IT, where A is a maximal monotone operator (nonlinear) from H into itself and v (specifically, I) are lower semicontinuous convex functions from H (specifically, H x H) to]-co,+ CXJ]. Here &I (specifically, al) denotes the subdifferential of CZJ (specifically of 1). It should be emphasized that Eqs.(1.1) and (1.2) include as special cases many other types of nonlinear two points boundary problems. For instance if z (u,, 2~~)= 4 (4+ h (d th en boundary condition (1.2) can be written under the familiar form aq+ hl/dt (o))-az,(u (o)) 3 0, aq@ u/dt (T))+ al& (T)) 3 0.(1.3)Other types of boundary conditions for Eq.(1.1) are implicitely incorporated into the problem through the condition Z (u (O), U (T))<+ co. The main existence result, Theorem 1, is stated in Section 3 and is proved in Section 4 by methods of convex analysis and monotone operators. This result may be compared with that obtained by the author [l] and with those of BrCzis [4] and Pave1 [ll]. In Section 5, via elliptic regularisation, one uses this result for obtaining an existence theorem for the evolution variational inequality