# Continuous dependence on parameters for second order discrete BVP’s

Open Mathematics (2012)

- Volume: 10, Issue: 3, page 1076-1083
- ISSN: 2391-5455

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topMarek Galewski, and Szymon Głąb. "Continuous dependence on parameters for second order discrete BVP’s." Open Mathematics 10.3 (2012): 1076-1083. <http://eudml.org/doc/269013>.

@article{MarekGalewski2012,

abstract = {Using Fan’s Min-Max Theorem we investigate existence of solutions and their dependence on parameters for some second order discrete boundary value problem. The approach is based on variational methods and solutions are obtained as saddle points to the relevant Euler action functional.},

author = {Marek Galewski, Szymon Głąb},

journal = {Open Mathematics},

keywords = {Continuous dependence on parameters; Min-Max Theorem; Critical point; Discrete BVP; continuous dependence on parameters; min-max theorem; critical point; second order discrete boundary value problem; variational methods; saddle points; Euler action functional},

language = {eng},

number = {3},

pages = {1076-1083},

title = {Continuous dependence on parameters for second order discrete BVP’s},

url = {http://eudml.org/doc/269013},

volume = {10},

year = {2012},

}

TY - JOUR

AU - Marek Galewski

AU - Szymon Głąb

TI - Continuous dependence on parameters for second order discrete BVP’s

JO - Open Mathematics

PY - 2012

VL - 10

IS - 3

SP - 1076

EP - 1083

AB - Using Fan’s Min-Max Theorem we investigate existence of solutions and their dependence on parameters for some second order discrete boundary value problem. The approach is based on variational methods and solutions are obtained as saddle points to the relevant Euler action functional.

LA - eng

KW - Continuous dependence on parameters; Min-Max Theorem; Critical point; Discrete BVP; continuous dependence on parameters; min-max theorem; critical point; second order discrete boundary value problem; variational methods; saddle points; Euler action functional

UR - http://eudml.org/doc/269013

ER -

## References

top- [1] Agarwal R.P., O’Regan D., A fixed-point approach for nonlinear discrete boundary value problems, Comput. Math. Appl., 1998, 36(10–12), 115–121 http://dx.doi.org/10.1016/S0898-1221(98)80014-X
- [2] Agarwal R.P., Perera K., O’Regan D., Multiple positive solutions of singular discrete p-Laplacian problems via variational methods, Adv. Difference Equ., 2005, 2, 93–99 Zbl1098.39001
- [3] Cai X., Yu J., Existence theorems of periodic solutions for second-order nonlinear difference equations, Adv. Difference Equ., 2008, #247071 Zbl1146.39006
- [4] Galewski M., Dependence on parameters for discrete second order boundary value problems, J. Difference Equ. Appl., 2011, 17(10), 1441–1453 http://dx.doi.org/10.1080/10236191003639442 Zbl1232.39007
- [5] Guo Y., Wei W., Chen Y., Existence of three positive solutions for m-point discrete boundary value problems with p-Laplacian, Discrete Dyn. Nat. Soc., 2009, #538431 Zbl1177.34031
- [6] Jakszto M., Skowron A., Existence of optimal controls via continuous dependence on parameters, Comput. Math. Appl., 2003, 46(10–11), 1657–1669 http://dx.doi.org/10.1016/S0898-1221(03)90200-8 Zbl1047.49002
- [7] Ledzewicz U., Schättler H., Walczak S., Optimal control systems governed by second-order ODEs with Dirichlet boundary data and variable parameters, Illinois J. Math., 2003, 47(4), 1189–1206 Zbl1031.49002
- [8] Lian F., Xu Y., Multiple solutions for boundary value problems of a discrete generalized Emden-Fowler equation, Appl. Math. Lett., 2010, 23(1), 8–12 http://dx.doi.org/10.1016/j.aml.2009.08.003 Zbl1191.39007
- [9] Mihăilescu M., Rădulescu V., Tersian S., Eigenvalue problems for anisotropic discrete boundary value problems, J. Difference Equ. Appl., 2009, 15(6), 557–567 http://dx.doi.org/10.1080/10236190802214977 Zbl1181.47016
- [10] Nirenberg L., Topics in Nonlinear Functional Analysis, Courant Lect. Notes Math., 6, American Mathematical Society, Providence, 2001 Zbl0992.47023
- [11] Tian Y., Du Z., Ge W., Existence results for discrete Sturm-Liouville problem via variational methods, J. Difference Equ. Appl., 2007, 13(6), 467–478 http://dx.doi.org/10.1080/10236190601086451 Zbl1129.39007
- [12] Zhang G., Existence of non-zero solutions for a nonlinear system with a parameter, Nonlinear Anal., 2007, 66(6), 1400–1416
- [13] Zhang G., Cheng S.S., Existence of solutions for a nonlinear system with a parameter, J. Math. Anal. Appl., 2006, 314(1), 311–319 http://dx.doi.org/10.1016/j.jmaa.2005.03.098 Zbl1087.39021