EXISTENCE AND UNIQUENESS OF NON-TRIVIAL SOLUTION OF PARABOLIC p-LAPLACIAN-LIKE DIFFERENTIAL EQUATION WITH MIXED BOUNDARIES

doi:10.1016/S0252-9602(16)30105-9

Acta mathematica scientia,Series B ›› 2016, Vol. 36 ›› Issue (6): 1780-1792.doi: 10.1016/S0252-9602(16)30105-9

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EXISTENCE AND UNIQUENESS OF NON-TRIVIAL SOLUTION OF PARABOLIC p-LAPLACIAN-LIKE DIFFERENTIAL EQUATION WITH MIXED BOUNDARIES

Li WEI¹, Rui CHEN¹, Ravi P. AGARWAL^2,3, Patricia YJ WONG⁴

1. School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, China;
2. Department of Mathematics, Texas A & M University-Kingsville, Kingsville, TX 78363, USA;
3. Department of Mathematics, Faculty of Science, King Abdulaziz University, 21589 Jeddah, Saudi Arabia;
4. School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore 639798, Singapore

Received:2015-04-13 Revised:2016-05-01 Online:2016-12-25 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).

Abstract

Abstract:

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.

Key words: maximal monotone operator, Caratheodory'conditions, subdifferential, p-Laplacian-like equation, nontrivial solution

CLC Number:

47H05

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.

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References

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EXISTENCE AND UNIQUENESS OF NON-TRIVIAL SOLUTION OF PARABOLIC p-LAPLACIAN-LIKE DIFFERENTIAL EQUATION WITH MIXED BOUNDARIES

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