On sequences of large homoclinic solutions for a difference equations on the integers

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• 作者：Robert Stegliński
• 关键词：39A10 ; 47J30 ; 35B38 ; difference equations ; discrete p ; Laplacian ; variational methods ; infinitely many solutions
• 刊名：Advances in Difference Equations
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：2016
• 期：1
• 全文大小：1,619 KB
• 参考文献：1. Agarwal, RP: On multipoint boundary value problems for discrete equations. J. Math. Anal. Appl. 96(2), 520-534 (1983) CrossRef MathSciNet MATH
  2. Sun, G: On standing wave solutions for discrete nonlinear Schrodinger equations. Abstr. Appl. Anal. 2013, Article ID 436919 (2013)
  3. Sun, G, Mai, A: Infinitely many homoclinic solutions for second order nonlinear difference equations with p-Laplacian. Sci. World J. 2014, Article ID 276372 (2014)
  4. Agarwal, RP, Perera, K, O’Regan, D: Multiple positive solutions of singular and nonsingular discrete problems via variational methods. Nonlinear Anal. 58, 69-73 (2004) CrossRef MathSciNet MATH
  5. Cabada, A, Iannizzotto, A, Tersian, S: Multiple solutions for discrete boundary value problems. J. Math. Anal. Appl. 356, 418-428 (2009) CrossRef MathSciNet MATH
  6. Candito, P, Molica Bisci, G: Existence of two solutions for a second-order discrete boundary value problem. Adv. Nonlinear Stud. 11, 443-453 (2011) MathSciNet MATH
  7. Galewski, M, Głab, S: On the discrete boundary value problem for anisotropic equation. Electron. J. Math. Anal. Appl. 386, 956-965 (2012) CrossRef MATH
  8. Mihăilescu, M, Rădulescu, V, Tersian, S: Eigenvalue problems for anisotropic discrete boundary value problems. J. Differ. Equ. Appl. 15(6), 557-567 (2009) CrossRef MATH
  9. Molica Bisci, G, Repovš, D: Existence of solutions for p-Laplacian discrete equations. Appl. Math. Comput. 242, 454-461 (2014) CrossRef MathSciNet
  10. Iannizzotto, A, Rădulescu, V: Positive homoclinic solutions for the discrete p-Laplacian with a coercive weight function. Differ. Integral Equ. 27(1-2), 35-44 (2014) MATH
  11. Iannizzotto, A, Tersian, S: Multiple homoclinic solutions for the discrete p-Laplacian via critical point theory. J. Math. Anal. Appl. 403, 173-182 (2013) CrossRef MathSciNet MATH
  12. Ma, M, Guo, Z: Homoclinic orbits for second order self-adjoint difference equations. J. Math. Anal. Appl. 323, 513-521 (2005) CrossRef MathSciNet
  13. Ricceri, B: A general variational principle and some of its applications. J. Comput. Appl. Math. 133, 401-410 (2000) CrossRef MathSciNet
  14. Bonanno, G, Molica Bisci, G: Infinitely many solutions for a Dirichlet problem involving the p-Laplacian. Proc. R. Soc. Edinb., Sect. A 140, 737-752 (2010) CrossRef MathSciNet MATH
  15. Bonanno, G, Candito, P: Infinitely many solutions for a class of discrete non-linear boundary value problems. Appl. Anal. 88, 605-616 (2009) CrossRef MathSciNet MATH
  16. Molica Bisci, G, Repovš, D: On sequences of solutions for discrete anisotropic equations. Expo. Math. 32, 284-295 (2014) CrossRef MathSciNet MATH
  17. Stegliński, R: On sequences of large solutions for discrete anisotropic equations. Electron. J. Qual. Theory Differ. Equ. 2015, 25 (2015) CrossRef
  18. Bonanno, G, Molica Bisci, G: Infinitely many solutions for a boundary value problem with discontinuous nonlinearities. Bound. Value Probl. 2009, Article ID 670675 (2009) CrossRef MathSciNet
  
• 作者单位：Robert Stegliński (1)
  
  1. Institute of Mathematics, Technical University of Lodz, Wolczanska 215, Lodz, 90-924, Poland
  
• 刊物主题：Difference and Functional Equations; Mathematics, general; Analysis; Functional Analysis; Ordinary Differential Equations; Partial Differential Equations;
• 出版者：Springer International Publishing
• ISSN：1687-1847

文摘

In this paper, we determine a concrete interval of positive parameters λ, for which we prove the existence of infinitely many homoclinic solutions for a discrete problem $$ -\Delta\phi_{p}\bigl(\Delta u(k-1)\bigr)+a(k)\phi_{p} \bigl(u(k)\bigr)=\lambda f\bigl(k,u(k)\bigr),\quad k\in\mathbb{Z}, $$