Geodesic
Existence and nonexistence of solutions for nonlinear second order q-integro-difference equations with non-separated boundary conditions :
Agarwal, Ravi P. 1   ; Wang, Guotao 2   ; Hobiny, Aatef 3   ; Zhang, Lihong 4   ; Ahmad, Bashir 3
1 Department of Mathematics, Texas A&M University, Kingsville, TX 78363-8202, USA;Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia
2 School of Mathematics and Computer Science, Shanxi Normal University, Linfen, Shanxi 041004, People's Republic of China
3 Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia
4 School of Mathematics and Computer Science, Shanxi Normal University, Linfen, Shanxi 041004, People's Republic of China
Journal of nonlinear sciences and its applications, Tome 8 (2015) no. 6, p. 976-985 Cet article a éte moissonné depuis la source International Scientific Research Publications

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In this paper, we investigate a nonlinear second order boundary value problem of q-integro-difference equations supplemented with non-separated boundary conditions. Sufficient conditions for the existence and nonexistence of solutions are presented. Examples are provided for explanation of the obtained work.

DOI : 10.22436/jnsa.008.06.08
Classification : 93C30, 93B18, 93A30, 39A99
Keywords: q-integro-difference equations, non-separated boundary conditions, existence, nonexistence.

Agarwal, Ravi P.  1   ; Wang, Guotao  2   ; Hobiny, Aatef  3   ; Zhang, Lihong  4   ; Ahmad, Bashir  3

1 Department of Mathematics, Texas A&M University, Kingsville, TX 78363-8202, USA;Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia
2 School of Mathematics and Computer Science, Shanxi Normal University, Linfen, Shanxi 041004, People's Republic of China
3 Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia
4 School of Mathematics and Computer Science, Shanxi Normal University, Linfen, Shanxi 041004, People's Republic of China 
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     title = {Existence and nonexistence of solutions for nonlinear second order q-integro-difference equations with non-separated boundary conditions},
     journal = {Journal of nonlinear sciences and its applications},
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Agarwal, Ravi P.; Wang, Guotao; Hobiny, Aatef; Zhang, Lihong; Ahmad, Bashir. Existence and nonexistence of solutions for nonlinear second order q-integro-difference equations with non-separated boundary conditions. Journal of nonlinear sciences and its applications, Tome 8 (2015) no. 6, p. 976-985. doi: 10.22436/jnsa.008.06.08

[1] Adams, C. R. On the linear ordinary q-difference equation, Ann. Math., Volume 30 (1928), pp. 195-205

[2] O. Agrawal Some generalized fractional calculus operators and their applications in integral equations, Fract. Calc. Appl. Anal., Volume 15 (2012), pp. 700-711

[3] Ahmad, B.; Ntouyas, S. K. Boundary value problems for q-difference inclusions, Abstr. Appl. Anal., Volume 2011 (2011), pp. 1-15

[4] Ahmad, B.; Alsaedi, A.; Ntouyas, S. K. A study of second-order q-difference equations with boundary conditions, Adv. Difference Equ., Volume 2012 (2012), pp. 1-10

[5] Ahmad, B.; Nieto, J. J. Basic theory of nonlinear third-order q-difference equations and inclusions, Math. Model. Anal., Volume 18 (2013), pp. 122-135

[6] Ahmad, B.; Ntouyas, S. K. Boundary value problems for q-difference equations and inclusions with nonlocal and integral boundary conditions, Math. Model. Anal., Volume 19 (2014), pp. 647-663

[7] Annaby, M. H.; Z. S. Mansour q-Fractional Calculus and Equations, Lecture Notes in Mathematics 2056, Springer- Verlag, 2012

[8] Aral, A.; Gupta, V.; Agarwal, R .P. Applications of q-Calculus in Operator Theory, Springer, New York, 2013

[9] Area, I.; Atakishiyev, N.; Godoy, E.; Rodal, J. Linear partial q-difference equations on q-linear lattices and their bivariate q-orthogonal polynomial solutions, Appl. Math. Comput., Volume 223 (2013), pp. 520-536

[10] Bangerezako, G. q-difference linear control systems, J. Difference Equ. Appl., Volume 17 (2011), pp. 1229-1249

[11] Bangerezako, G. Variational q-calculus, J. Math. Anal. Appl., Volume 289 (2004), pp. 650-665

[12] Bartosiewicz, Z.; Pawluszewicz, E. Realizations of linear control systems on time scales, Control Cybernet., Volume 35 (2006), pp. 769-786

[13] Bohner, M.; Chieochan, R. Floquet theory for q-difference equations, Sarajevo J. Math., Volume 8 (2012), pp. 355-366

[14] R. D. Carmichael The general theory of linear q-difference equations, Amer. J. Math., Volume 34 (1912), pp. 147-168

[15] El-Shahed, M.; Hassan, H. A. Positive solutions of q-difference equation, Proc. Amer. Math. Soc., Volume 138 (2010), pp. 1733-1738

[16] Gasper, G.; M. Rahman Basic Hypergeometric Series, Cambridge University Press, Cambridge, 1990

[17] Ismail, M. E. H.; Simeonov, P. q-difference operators for orthogonal polynomials, J. Comput. Appl. Math., Volume 233 (2009), pp. 749-761

[18] Jackson, F. H. On q-functions and a certain difference operator, Trans. Roy. Soc. Edinburgh, Volume 46 (1909), pp. 253-281

[19] Jackson, F. H. On q-difference equations, Amee. J. Math., Volume 32 (1910), pp. 305-314

[20] Kac, V.; P. Cheung Quantum Calculus, Springer, New York, 2002

[21] Krasnosel'ski, M. A.; Zabreiko, P. P. Geometrical Methods of Nonlinear Analysis, Springer-Verlag, Berlin, 1984

[22] Mason, T. E. On properties of the solutions of linear q-difference equations with entire function coefficients, Amer. J. Math., Volume 37 (1915), pp. 439-444

[23] Mozyrska, D.; Bartosiewicz, Z. On Observability of Nonlinear Discrete-Time Fractional-Order Control Systems, New Trends in Nanotechnology and Fractional Calculus Applications (2010), pp. 305-312

[24] Pongarm, N.; Asawasamrit, S.; Tariboon, J. Sequential derivatives of nonlinear q-difference equations with three- point q-integral boundary conditions, J. Appl. Math., Volume 2013 (2013), pp. 1-9

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