Journal of Northeastern University ›› 2007, Vol. 28 ›› Issue (6): 891-894.DOI: -

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Existence and multisolvability of sign-inversing solution to nonlinear operator equations and their applications

Sun, Tao (1); Meng, Peng (2); Duan, Xiao-Dong (3)   

  1. (1) School of Sciences, Northeastern University, Shenyang 110004, China; (2) Mathematics Department, Bohai University, Jinzhou 121000, China; (3) Institute of Nonlinear Information Technology, Dalian Nationalities University, Dalian 116600, China
  • Received:2013-06-24 Revised:2013-06-24 Online:2007-06-15 Published:2013-06-24
  • Contact: Sun, T.
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Abstract: The existence and multisolvability of the sign-inversing solution to nonlinear operator equations are discussed, based on the cone theory and fixed point theory in Banach space. An existence theorem of sign-inversing solution is proved by an upper bound solution, further, the four solutions, i.e. positive, negative, null and sign-inversing solutions, are obtained through an upper bound solution and a lower solution. Then, the existence of both the sign-inversing solution and the four solutions are discussed in detail for a kind of important nonlinear operator equations, i.e. the Sturm-Liouville two-point boundary value problems and, correspondingly the theorems of the existence of both the solutions as above are proved. An example is given to illustrate their applications.

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