Publication Cover
Applicable Analysis
An International Journal
Volume 88, 2009 - Issue 4
145
Views
60
CrossRef citations to date
0
Altmetric
Original Articles

Infinitely many solutions for a class of discrete non-linear boundary value problems

&
Pages 605-616 | Received 06 Feb 2009, Accepted 23 Mar 2009, Published online: 16 Jun 2009

References

  • Chu , J and Jiang , D . 2005 . Eigenvalues and discrete boundary value problems for the one-dimensional p-Laplacian . J. Math. Anal. Appl. , 305 : 452 – 465 .
  • Jiang , D , Chu , J , O'Regan , D and Agarwal , RP . 2004 . Positive solutions for continuous and discrete boundary value problems to the one-dimensional p-Laplacian . Math. Inequal. Appl. , 7 : 523 – 534 .
  • Henderson , J and Thompson , HB . 2002 . Existence of multiple solutions for second order discrete boundary value problems . Comput. Math. Appl. , 43 : 1239 – 1248 .
  • Bai , D and Xu , Y . 2007 . Nontrivial solutions of boundary value problems of second-order difference equations . J. Math. Anal. Appl. , 326 : 297 – 302 .
  • Bonanno , G and Candito , P . 2009 . Nonlinear difference equations investigated via critical points methods . Nonlinear Anal. , 70 : 3180 – 3186 .
  • Candito , P and Giovannelli , N . 2008 . Multiple solutions for a discrete boundary value problem . Comput. Math. Appl. , 56 : 959 – 964 .
  • Faraci , F and Iannizzotto , A . 2007 . Multiplicity theorems for discrete boundary problems . Aequationes Math. , 74 : 111 – 118 .
  • Jiang , L and Zhou , Z . 2008 . Three solutions to Dirichlet boundary value problems for p-Laplacian difference equations . Adv. Diff. Equ. , 2008 : 1 – 10 .
  • Liang , H and Weng , P . 2007 . Existence and multiple solutions for a second-order difference boundary value problem via critical point theory . J. Math. Anal. Appl. , 326 : 511 – 520 .
  • Zhang , G and Liu , S . 2007 . On a class of semipositone discrete boundary value problems . J. Math. Anal. Appl. , 325 : 175 – 182 .
  • Agarwal , RP , Perera , K and O'Regan , D . 2005 . Multiple positive solutions of singular discrete p-Laplacian problems via variational methods . Adv. Diff. Equ. , 2 : 93 – 99 .
  • Agarwal , RP , Perera , K and O'Regan , D . 2004 . Multiple positive solutions of singular and nonsingular discrete problems via variational methods . Nonlinear Anal. , 58 : 69 – 73 .
  • Bonanno , G and Bisci , GMolica . 2009 . Bound. Value Probl. 2009 . Infinitely many solutions for a boundary value problem with discontinuous nonlinearities , : 1 – 20 .
  • Marano , SA and Motreanu , D . 2002 . Infinitely many critical points of non-differentiable functions and applications to a Neumann type problem involving the p-Laplacian . J. Diff. Equ. , 182 : 108 – 120 .
  • Ricceri , B . 2000 . A general variational principle and some of its applications . J. Comput. Appl. Math. , 133 : 401 – 410 .
  • Bonanno , G and Candito , P . 2008 . Non-differentiable functions with applications to elliptic equations with discontinuous nonlinearities . J. Diff. Equ. , 244 ( 12 ) : 3031 – 3059 .
  • Agarwal , RP . 2000 . Difference Equations and Inequalities: Theory, Methods and Applications , New York, Basel : Marcel Dekker .
  • Agarwal , RP , O'Regan , D and Wong , PJY . 1999 . Positive Solutions of Differential, Difference and Integral Equations , Dordrecht : Kluwer Academic Publishers .
  • Kelly , WG and Peterson , AC . 1991 . Difference Equations, An Introduction with Applications , San Diego, New York : Academic Press .
  • Rabinowitz , PH . Minimax Methods in Critical Point Theory with Applications to Differential Equations . CBMS Regional Conferences in Mathematics . Vol. 65 , Providence, RI : American Mathematical Society .
  • Struwe , M . 1996 . Variational Methods , Berlin : Springer .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.