Study on the generalized \((p,q)\) -Laplacian elliptic systems, parabolic systems and integro-differential systems

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• 作者：Li Wei ; Ravi P Agarwal ; Patricia JY Wong
• 关键词：47H05 ; 47H09 ; maximal monotone operator ; coercive ; ( p ; q ) $(p ; q)$ ; Laplacian ; parabolic systems ; elliptic systems ; integro ; differential systems
• 刊名：Boundary Value Problems
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：2016
• 期：1
• 全文大小：1,788 KB
• 参考文献：1. Calvert, BD, Gupta, CP: Nonlinear elliptic boundary value problems in \(L^{p}\) -spaces and sums of ranges of accretive operators. Nonlinear Anal. 2, 1-26 (1978) MATH MathSciNet CrossRef
  2. Wei, L, Agarwal, RP: Existence of solutions to nonlinear Neumann boundary value problems with generalized p-Laplacian operator. Comput. Math. Appl. 56, 530-541 (2008) MATH MathSciNet CrossRef
  3. Wei, L, Agarwal, RP, Wong, PJY: Results on the existence of solution of p-Laplacian-like equation. Adv. Math. Sci. Appl. 23(1), 153-167 (2013) MATH MathSciNet
  4. Wei, L, Agarwal, RP, Wong, PJY: Applications of perturbations on accretive mappings to nonlinear elliptic systems involving \((p,q)\) -Laplacian. Nonlinear Oscil. 12, 199-212 (2009) MATH MathSciNet CrossRef
  5. Brezis, H: Équations et inéqualitions nonlinéares dans les espaces vectoriels an dualité. Ann. Inst. Fourier (Grenoble) 18, 115-175 (1968) MATH MathSciNet CrossRef
  6. Wei, L, Liu, YX, Agarwal, RP: Existence and iterative construction of solutions for nonlinear Dirichlet elliptic systems involving \((p,q)\) -Laplacian. Math. Appl. 25(2), 246-252 (2012) MATH MathSciNet
  7. Wei, L, Agarwal, RP, Wong, PJY: Study on integro-differential equation with generalized p-Laplacian operator. Bound. Value Probl. 2012, 131 (2012) MathSciNet CrossRef
  8. Zeidler, E: Nonlinear Functional Analysis and Its Applications. IIA: Linear Monotone Operators. Springer, New York (1990) CrossRef
  9. Wei, L, Agarwal, RP, Wong, PJY: Discussion on the existence and uniqueness of solution to nonlinear integro-differential systems. Comput. Math. Appl. 69, 374-389 (2015) MathSciNet CrossRef
  10. Zeng, LC, Guu, SM, Yao, JC: Characterization of H-monotone operators with applications to variational inclusions. Comput. Math. Appl. 50, 329-337 (2005) MATH MathSciNet CrossRef
  11. Wei, L, Agarwal, RP, Wong, PJY: Existence of solutions to nonlinear parabolic boundary value problems with generalized p-Laplacian operator. Adv. Math. Sci. Appl. 20(2), 423-445 (2010) MATH MathSciNet
  12. Reich, S: The range of sums of accretive and monotone operators. J. Math. Anal. Appl. 68, 310-317 (1979) MATH MathSciNet CrossRef
  13. Barbu, V: Nonlinear Semigroups and Differential Equations in Banach Spaces. Noordhoff, Leyden (1976) MATH CrossRef
  14. Pascali, R, Sburlan, S: Nonlinear Mappings of Monotone Type. Sijthoff & Noordhoff, Alphen aan den Rijn (1978) MATH CrossRef
  15. Kato, T: Perturbation Theory for Linear Operators. Springer, Berlin (1984) MATH
  16. Wei, L, Duan, LL, Zhou, HY: Solution of nonlinear elliptic boundary value problems and its iterative construction. Abstr. Appl. Anal. 2012, Article ID 210325 (2012) MathSciNet
  17. Chao, C, Yang, J: Nonnegative solutions for asymptotically linear elliptic systems. Appl. Math. 22, 603-609 (2009)
  18. Chen, Z, Luo, T: The initial-boundary value problem for quasilinear integro-differential equations. Int. J. Differ. Equ. Appl. 6(3), 299-306 (2002) MATH MathSciNet
  
• 作者单位：Li Wei (1)
  Ravi P Agarwal (2) (3)
  Patricia JY Wong (4)
  
  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, Jeddah, 21589, Saudi Arabia
  4. School of Electrical and Electronic Engineering, Nanyang Technological University, 50 Nanyang Avenue, Singapore, 639798, Singapore
  
• 刊物主题：Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations; Analysis; Approximations and Expansions; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1687-2770

文摘

In this paper, we present the abstract results for the existence and uniqueness of the solution of nonlinear elliptic systems, parabolic systems and integro-differential systems involving the generalized \((p,q)\)-Laplacian operator. Our method makes use of the characteristics of the ranges of linear and nonlinear maximal monotone operators and the subdifferential of a proper, convex, and lower-semi-continuous functional, and we employ some new techniques in the construction of the operators and in proving the properties of the newly defined operators. The systems discussed in this paper and the method used extend and complement some of the previous work. Keywords maximal monotone operator coercive \((p,q)\)-Laplacian parabolic systems elliptic systems integro-differential systems