Geodesic
Singular $\phi $-Laplacian third-order BVPs with derivative dependance
Archivum mathematicum, Tome 52 (2016) no. 1, pp. 35-48 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

This work is devoted to the existence of solutions for a class of singular third-order boundary value problem associated with a $\phi $-Laplacian operator and posed on the positive half-line; the nonlinearity also depends on the first derivative. The upper and lower solution method combined with the fixed point theory guarantee the existence of positive solutions when the nonlinearity is monotonic with respect to its arguments and may have a space singularity; however no Nagumo type condition is assumed. An example of application illustrates the applicability of the existence result.
This work is devoted to the existence of solutions for a class of singular third-order boundary value problem associated with a $\phi $-Laplacian operator and posed on the positive half-line; the nonlinearity also depends on the first derivative. The upper and lower solution method combined with the fixed point theory guarantee the existence of positive solutions when the nonlinearity is monotonic with respect to its arguments and may have a space singularity; however no Nagumo type condition is assumed. An example of application illustrates the applicability of the existence result.
DOI : 10.5817/AM2016-1-35
Classification : 34B15, 34B18, 34B40, 47H10
Keywords: third order; half-line; $\phi $-Laplacian; singular problem; positive solution; derivative dependance; upper and lower solution 
@article{10_5817_AM2016_1_35,
     author = {Djebali, Sma{\"\i}l and Saifi, Ouiza},
     title = {Singular $\phi ${-Laplacian} third-order {BVPs} with derivative dependance},
     journal = {Archivum mathematicum},
     pages = {35--48},
     year = {2016},
     volume = {52},
     number = {1},
     doi = {10.5817/AM2016-1-35},
     mrnumber = {3475111},
     zbl = {06562207},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.5817/AM2016-1-35/}
}
TY  - JOUR
AU  - Djebali, Smaïl
AU  - Saifi, Ouiza
TI  - Singular $\phi $-Laplacian third-order BVPs with derivative dependance
JO  - Archivum mathematicum
PY  - 2016
SP  - 35
EP  - 48
VL  - 52
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.5817/AM2016-1-35/
DO  - 10.5817/AM2016-1-35
LA  - en
ID  - 10_5817_AM2016_1_35
ER  - 
%0 Journal Article
%A Djebali, Smaïl
%A Saifi, Ouiza
%T Singular $\phi $-Laplacian third-order BVPs with derivative dependance
%J Archivum mathematicum
%D 2016
%P 35-48
%V 52
%N 1
%U http://geodesic.mathdoc.fr/articles/10.5817/AM2016-1-35/
%R 10.5817/AM2016-1-35
%G en
%F 10_5817_AM2016_1_35
Djebali, Smaïl; Saifi, Ouiza. Singular $\phi $-Laplacian third-order BVPs with derivative dependance. Archivum mathematicum, Tome 52 (2016) no. 1, pp. 35-48. doi: 10.5817/AM2016-1-35

[1] Agarwal, R.P., Meehan, M., O’Regan, D.: Fixed Point Theory and Applications. Cambridge Tracts in Mathematics, vol. 141, Cambridge University Press, 2001. | DOI | MR | Zbl

[2] Agarwal, R.P., O’Regan, D.: Infinite Interval Problems for Differential, Difference, and Integral Equations. Kluwer Academic Publishers, Dordrecht, 2001. | MR | Zbl

[3] Corduneanu, C.: Integral Equations and Stability of Feedback Systems. vol. 104, Academic Press, New York, 1973. | MR | Zbl

[4] Djebali, S., Mebarki, K.: Multiple positive solutions for singular BVPs on the positive half-line. Comput. Math. Appl. 55 (112) (2008), 2940–2952. | DOI | MR | Zbl

[5] Djebali, S., Mebarki, K.: On the singular generalized Fisher-like equation with derivative depending nonlinearity. Appl. Math. Comput. 205 (1) (2008), 336–351. | DOI | MR | Zbl

[6] Djebali, S., Mebarki, K.: Multiple unbounded positive solutions for three-point bvps with sign-changing nonlinearities on the positive half-line. Acta Appl. Math. 109 (2) (2010), 361–388. | DOI | MR | Zbl

[7] Djebali, S., Saifi, O.: Positive solutions for singular $\phi $-Laplacian BVPs on the positive half-line. EJQTDE (56) (2009), 24pp. | MR | Zbl

[8] Djebali, S., Saifi, O.: Positive solutions for singular BVPs on the positive half-line with sign changing and derivative depending nonlinearity. Acta Appl. Math. 110 (2) (2010), 639–665. | DOI | MR

[9] Djebali, S., Saifi, O.: Upper and lower solution method for singular $\phi -$Laplacian BVPs with derivative depending nonlinearity on $[0,+\infty )$. Commun. Appl. Anal. 14 (4) (2010), 463–480. | MR

[10] Djebali, S., Saifi, O.: Third order BVPs with $\phi $-Laplacian operators on $[0,+\infty )$. Afr. Diaspora J. Math. 16 (1) (2013), 1–17. | MR | Zbl

[11] Djebali, S., Saifi, O.: Upper and lower solutions for $\phi $-Laplacian third-order BVPs on the half-line. Cubo 16 (1) (2014), 105–116. | DOI | MR | Zbl

[12] Guo, Y., Yu, C., Wang, J.: Existence of three positive solutions for $m$-point boundary value problems on infinite intervals. Nonlinear Anal. 71 (3–4) (2009), 717–722. | DOI | MR | Zbl

[13] Han, G., Li, F.: Multiple solutions of some fourth-order boundary value problems. Nonlinear Anal. 66 (11) (2007), 2591–2603. | DOI | MR | Zbl

[14] Liang, S., Zhang, J.: Positive solutions for singular third-order boundary-value problem with dependence on the first order derivative on the half-line. Acta Appl. Math. 111 (1) (2010), 27–43. | DOI | MR | Zbl

[15] Tian, Y., Ge, W., Shan, W.: Positive solutions for three-point boundary value problem on the half-line. Comput. Math. Appl. 53 (7) (2007), 1029–1039. | DOI | MR | Zbl

[16] Yan, B., Liu, Y.: Unbounded solutions of the singular boundary value problems for second order differential equations on the half-line. Appl. Math. Comput. 147 (3) (2004), 629–644. | DOI | MR | Zbl

[17] Yan, B., O’Regan, D., Agarwal, R.P.: Positive solutions for second order singular boundary value problems with derivative dependence on infinite intervals. Acta Appl. Math. 103 (1) (2008), 19–57. | MR | Zbl

[18] Yang, Y., Zhang, J.: Existence of solutions for some fourth-order boundary value problems with parameters. Nonlinear Anal. 69 (4) (2008), 1364–1375. | DOI | MR | Zbl

[19] Yang, Y., Zhang, J.: Nontrivial solutions for some fourth order boundary value problems with parameters. Nonlinear Anal. 70 (11) (2009), 3966–3977. | DOI | MR | Zbl

Cité par Sources :