Volume 7, Issue 2
Existence of Global and Periodic Solutions for Delay Equation with Quasilinear Perturbation

Xiang Xiaoling

J. Part. Diff. Eq.,7(1994),pp.171-182

Published online: 1994-07

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  • Abstract
Delay parabolic problems have been studied by many authors. Some authors investigated more general delay problem (refer to [1], [2]), some investigated concrete delay partial differential equations. Recently, we have done some work on delay parabolic problem. We discussed semilinear parabolic delay problem and obtained some results on the existence of solutions. In particular the results on existence of periodic solutions are characteristic (see [3], [4], [5], [6]). The purpose of this paper is to study delay equation with quasilinear perturbation. We present the existence of global and periodic solutions of abstract evolution equations in Section 2. The abstract results are used to obtain the existence of global and periodic solutions of delay parabolic problem with quasilinear perturbation in Section 3. We make preparation for our investigation and give a generalization of Gronwall inequality (Lemma 1.3) which is used in next section.
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@Article{JPDE-7-171, author = {Xiang Xiaoling}, title = {Existence of Global and Periodic Solutions for Delay Equation with Quasilinear Perturbation}, journal = {Journal of Partial Differential Equations}, year = {1994}, volume = {7}, number = {2}, pages = {171--182}, abstract = { Delay parabolic problems have been studied by many authors. Some authors investigated more general delay problem (refer to [1], [2]), some investigated concrete delay partial differential equations. Recently, we have done some work on delay parabolic problem. We discussed semilinear parabolic delay problem and obtained some results on the existence of solutions. In particular the results on existence of periodic solutions are characteristic (see [3], [4], [5], [6]). The purpose of this paper is to study delay equation with quasilinear perturbation. We present the existence of global and periodic solutions of abstract evolution equations in Section 2. The abstract results are used to obtain the existence of global and periodic solutions of delay parabolic problem with quasilinear perturbation in Section 3. We make preparation for our investigation and give a generalization of Gronwall inequality (Lemma 1.3) which is used in next section.}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5680.html} }
TY - JOUR T1 - Existence of Global and Periodic Solutions for Delay Equation with Quasilinear Perturbation AU - Xiang Xiaoling JO - Journal of Partial Differential Equations VL - 2 SP - 171 EP - 182 PY - 1994 DA - 1994/07 SN - 7 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5680.html KW - AB - Delay parabolic problems have been studied by many authors. Some authors investigated more general delay problem (refer to [1], [2]), some investigated concrete delay partial differential equations. Recently, we have done some work on delay parabolic problem. We discussed semilinear parabolic delay problem and obtained some results on the existence of solutions. In particular the results on existence of periodic solutions are characteristic (see [3], [4], [5], [6]). The purpose of this paper is to study delay equation with quasilinear perturbation. We present the existence of global and periodic solutions of abstract evolution equations in Section 2. The abstract results are used to obtain the existence of global and periodic solutions of delay parabolic problem with quasilinear perturbation in Section 3. We make preparation for our investigation and give a generalization of Gronwall inequality (Lemma 1.3) which is used in next section.
Xiang Xiaoling. (1970). Existence of Global and Periodic Solutions for Delay Equation with Quasilinear Perturbation. Journal of Partial Differential Equations. 7 (2). 171-182. doi:
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