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Multiple Solutions for Resonant Difference Equations

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Book cover Web Information Systems and Mining (WISM 2011)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 6988))

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Abstract

In this paper, the critical point theory, the minimax methods and Morse theory are employed to discuss the existence of nontrivial solutions for boundary value problems of second-order difference equations with resonance both at infinity and at zero. Some existence results are obtained.

The project is supported by the National Science Foundation of Shanxi (No. 2011011002–4).

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References

  1. Agarwal, R.P., Perera, K., O’Regan, D.: Multiple positive solutions of singular discrete p-Laplacian problems via variational methods. Adv. Difference Equ. 2, 93–99 (2005)

    MathSciNet  MATH  Google Scholar 

  2. Bartsch, T., Li, S.J.: Critical point theory for asympotically quadratic functional and application to the problems with resonance. Nonlinear Anal. 28, 419–441 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bonanno, G., Candito, P.: Infinitely many solutions for a class of discrete non-linear boundary value problems. Appl. Anal. 88, 605–616 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bonanno, G., Candito, P.: Nonlinear difference equations investigated via critical point methods. Nonlinear Anal. 70, 3180–3186 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  5. Candito, P., Giovannelli, N.: Multiple solutions for a discrete boundary value problem involving the p-Laplacian. Comput. Math. Appl. 56, 959–964 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Cerami, G.: An existence criterion for the critical points on unbounded manifolds. Isit. Lombardo Accaqd. Sci. Lett. Rend. A 112, 332–336 (1978) (in Italian)

    MathSciNet  MATH  Google Scholar 

  7. Chang, K.C.: Infinite Dimensional Morse Theory and Multiple Solutions Problems. Birkhauser, Boston (1993)

    Book  Google Scholar 

  8. Chang, K.C.: H1 versus C1 isolated critical points. C. R. Acad. Sci. Paris 319, 441–446 (1994)

    Google Scholar 

  9. Jiang, L., Zhou, Z.: Existence of nontrivial solutions for discrete nonlinear two point boundary value problems. Appl. Math. Comput. 180, 318–329 (2006)

    MathSciNet  MATH  Google Scholar 

  10. Li, S., Liu, J.Q.: Some existence theorems on multiple critical points and their applications. Kexue Tongbao 17, 1025–1027 (1984)

    Google Scholar 

  11. Li, S.J., Willem, M.: Applications of local linking to critical point theory. J. Math. Anal. Appl. 189, 6–32 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  12. Liu, J.Q.: A Morse index for a saddle point. Syst. Sci. Math. Sci. 2, 32–39 (1989)

    MathSciNet  MATH  Google Scholar 

  13. Liu, J.S., Wang, S.L., Zhang, J.M.: Multiple solutions for boundary value problems of second-order difference equations with resonance. J. Math. Anal. Appl. 374, 187–196 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  14. Rabinowitz, P.: Minimax methods in critical point theory with applications for differential equations. In: CBMS Regional Conference (1984)

    Google Scholar 

  15. Wang, D., Guan, W.: Three positive solutions of boundary value problems for p-Laplacian difference equations. Comput. Math. Appl. 55, 1943–1949 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  16. Zhu, B.S., Yu, J.S.: Multiple positive solutions for resonant difference equations. Math. Comput. Modelling 49, 1928–1936 (2009)

    Article  MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, Taiyuan University of Technology, Taiyuan, Shanxi, 030024, P.R. China

    Shuli Wang & Jianming Zhang

Authors
  1. Shuli Wang
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  2. Jianming Zhang
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Editor information

Editors and Affiliations

  1. Department of Computer and Inforamtion Science, University of Macau, Av. Padre Tomás Pereira, Taipa, Macau, China

    Zhiguo Gong

  2. School of Computer, Shanghai University, 200444, Shanghai, China

    Xiangfeng Luo

  3. College of Computer and Software, Taiyuan University of Technology, 030024, Taiyuan, China

    Junjie Chen

  4. School of Computer and Information Engineering, Shanghai University of Electric Power, 200090, Shanghai, China

    Jingsheng Lei

  5. Department of Business Administration, Caritas Institute of Higher Education, 18 Chui Ling Road, Tseung Kwan O, Hong Kong, China

    Fu Lee Wang

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© 2011 Springer-Verlag Berlin Heidelberg

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Wang, S., Zhang, J. (2011). Multiple Solutions for Resonant Difference Equations. In: Gong, Z., Luo, X., Chen, J., Lei, J., Wang, F.L. (eds) Web Information Systems and Mining. WISM 2011. Lecture Notes in Computer Science, vol 6988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23982-3_8

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  • DOI: https://doi.org/10.1007/978-3-642-23982-3_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-23981-6

  • Online ISBN: 978-3-642-23982-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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