Skip to main content
SpringerLink
Log in

Two Positive Solutions for a Nonlinear Neumann Problem Involving the Discrete p-Laplacian

  • Conference paper
  • First Online:
Differential and Difference Equations with Applications (ICDDEA 2019)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 333))

Abstract

This paper is devoted to study of existence of at least two positive solutions for a nonlinear Neumann boundary value problem involving the discrete p-Laplacian.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 249.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Agarwal, R.P., Perera, K., O’Regan, D.: Multiple positive solutions of singular and nonsingular discrete problems via variational methods. Nonlinear Anal. 58, 69–73 (2004)

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  3. Agarwal, R.P.: On multipoint boundary value problems for discrete equations. J. Math. Anal. Appl. 96(2), 520–534 (1983)

    MathSciNet  MATH  Google Scholar 

  4. Ambrosetti, A., Rabinowitz, P.H.: Dual variational methods in critical point theory and applications. J. Funct. Anal. 14, 349–381 (1973)

    MathSciNet  MATH  Google Scholar 

  5. Anderson, D.R., Rachuånková, I., Tisdell, C.C.: Solvability of discrete Neumann boundary value probles. Adv. Diff. Equ. 2, 93–99 (2005)

    Google Scholar 

  6. Bonanno, G., D’Aguì, G.: Two non-zero solutions for elliptic Dirichlet problems. Z. Anal. Anwend. 35(4), 449–464 (2016)

    MathSciNet  MATH  Google Scholar 

  7. C. Bereanu, J. Mawhin, Boundary value problems for second-order nonlinear difference equations with discrete\(\phi \)-Laplacian and singular \(\phi \), J. Difference Equ. Appl. 14 (2008), 1099–1118

    Google Scholar 

  8. C. Bereanu, P. Jebelean, C. Şerban, Ground state and mountain pass solutions for discrete \(p(\cdot )-\)Laplacian, Bound. Value Probl. 2012 (104) (2012)

    Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  11. Bonanno, G., Candito, P.: Nonlinear difference equations through variational methods, Handbook on Nonconvex Analysis, pp. 1–44. Int. Press, Somerville, MA (2010)

    MATH  Google Scholar 

  12. Bonanno, G., Candito, P., D’Aguì, G.: Variational methods on finite dimensional Banach spaces and discrete problems. Advanced Nonlinear Studies 14, 915–939 (2014)

    MathSciNet  MATH  Google Scholar 

  13. Bonanno, G.: A critical point theorem via the Ekeland variational principle. Nonlinear Anal. 75, 2992–3007 (2012)

    MathSciNet  MATH  Google Scholar 

  14. Bonanno, G., Jebelean, P., Şerban, C.: Superlinear discrete problems. Appl. Math. Lett. 52, 162–168 (2016)

    MathSciNet  MATH  Google Scholar 

  15. P. Candito, G. D’Aguì, Three solutions for a discrete nonlinear Neumann problem involving the p-Laplacian, Adv. Difference Equ. 2010, Art. ID 862016, 11 pp

    Google Scholar 

  16. Candito, P., D’Aguì, G.: Three solutions to a perturbed nonlinear discrete Dirichlet problem. J. Math. Anal. Appl. 375, 594–601 (2011)

    MathSciNet  MATH  Google Scholar 

  17. Candito, P., D’Aguì, G.: Constant-sign solutions for a nonlinear neumann problem involving the discrete p-laplacian. Opuscula Math. 34(4), 683–690 (2014)

    MathSciNet  MATH  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  19. G. D’Aguì, J. Mawhin, A. Sciammetta Positive solutions for a discrete two point nonlinear boundary value problem with p-Laplacian, J. Math. Anal.Appl. 447, (2017),383–397

    Google Scholar 

  20. M. Galewski, S. Gla̧b, On the discrete boundary value problem for anisotropic equation, J. Math. Anal. Appl. 386 (2012), 956–965

    Google Scholar 

  21. A. Guiro, I. Nyanquini, S. Ouaro, On the solvability of discrete nonlinear Neumann problems involving the p(x)-Laplacian, Adv. Difference Equ. 2011 (32) (2011)

    Google Scholar 

  22. L. Jiang, Z. Zhou, Three solutions to Dirichlet boundary value problems for p-Laplacian difference equations, Adv. Difference Equ. (2008). Article ID 345916, 10 p

    Google Scholar 

  23. Rachuånková, I., Tisdell, C.C.: Existence of non-spurious solutions to discrete Dirichlet problems with lower and upper solutions. Nonlinear Anal. 67, 1236–1245 (2007)

    MathSciNet  MATH  Google Scholar 

  24. Şerban, C.: Existence of solutions for discrete p-Laplacian with potential boundary conditions. J. Difference Equ. Appl. 19, 527–537 (2013)

    MathSciNet  MATH  Google Scholar 

  25. Tian, Y., Ge, W.: The existence of solutions for a second-order discrete Neumann problem with p-Laplacian. J. Appl. Math. Comput. 26, 333–340 (2008)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

The authors are members of the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM). The paper is partially supported by PRIN 2017 - Progetti di Ricerca di rilevante Interesse Nazionale, “Nonlinear Differential Problems via Variational, Topological and Set-valued Methods” (2017AYM8XW).

Author information

Authors and Affiliations

  1. Department of Engineering, University of Messina, Contrada Di Dio (S. Agata), 98166, Messina, Italy

    G. Bonanno & G. D’Aguì

  2. Department DICEAM, University of Reggio Calabria, Via Graziella (Feo Di Vito), 89122, Reggio Calabria, Italy

    P. Candito

Authors
  1. G. Bonanno
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. Candito
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. G. D’Aguì
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. D’Aguì .

Editor information

Editors and Affiliations

  1. Department of Exact Sciences and Engineering, Military Academy, Lisbon, Portugal

    Sandra Pinelas

  2. Department of Mathematics, University of Tennessee at Chattanooga, Chattanooga, TN, USA

    John R. Graef

  3. Mathematik und Didaktik, Katholische Universität Eichstätt, Eichstätt, Bayern, Germany

    Stefan Hilger

  4. Huazhong University of Science and Technology, Wuhan, Hubei, China

    Peter Kloeden

  5. Department of Electrical and Computer Engineering, Democritus University of Thrace, Xanthi, Xanthi, Greece

    Christos Schinas

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Bonanno, G., Candito, P., D’Aguì, G. (2020). Two Positive Solutions for a Nonlinear Neumann Problem Involving the Discrete p-Laplacian. In: Pinelas, S., Graef, J.R., Hilger, S., Kloeden, P., Schinas, C. (eds) Differential and Difference Equations with Applications. ICDDEA 2019. Springer Proceedings in Mathematics & Statistics, vol 333. Springer, Cham. https://doi.org/10.1007/978-3-030-56323-3_23

Download citation

Publish with us

Policies and ethics

Search

Navigation