Acta mathematica scientia, Series B >
EXISTENCE AND UNIQUENESS OF NON-TRIVIAL SOLUTION OF PARABOLIC p-LAPLACIAN-LIKE DIFFERENTIAL EQUATION WITH MIXED BOUNDARIES
Received date: 2015-04-13
Revised date: 2016-05-01
Online published: 2016-12-25
Supported by
The first author is supported by the National Natural Science Foundation of China (11071053), Natural Science Foundation of Hebei Province (A2014207010), Key Project of Science and Research of Hebei Educational Department (ZD2016024) and Key Project of Science and Research of Hebei University of Economics and Business (2015KYZ03).
One parabolic p-Laplacian-like differential equation with mixed boundaries is studied in this paper, where the item ((∂u)/(∂t)) in the corresponding studies is replaced by α(((∂u)/(∂t))), which makes it more general. The sufficient condition of the existence and uniqueness of non-trivial solution in L2(0, T; L2(Ω)) is presented by employing the techniques of splitting the boundary problems into operator equation. Compared to the corresponding work, the restrictions imposed on the equation are weaken and the proof technique is simplified. It can be regarded as the extension and complement of the previous work.
Li WEI , Rui CHEN , Ravi P. AGARWAL , Patricia YJ WONG . EXISTENCE AND UNIQUENESS OF NON-TRIVIAL SOLUTION OF PARABOLIC p-LAPLACIAN-LIKE DIFFERENTIAL EQUATION WITH MIXED BOUNDARIES[J]. Acta mathematica scientia, Series B, 2016 , 36(6) : 1780 -1792 . DOI: 10.1016/S0252-9602(16)30105-9
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