Geodesic
POSITIVE SOLUTIONS FOR A CLASS OF SINGULAR TWO POINT BOUNDARY VALUE PROBLEMS
KHAN, RAHMAT ALI1 ; ASIF, NASEER AHMAD1
1 Centre for Advanced Mathematics and Physics, National University of Sciences and Technology, Campus of College of Electrical and Mechanical Engineering, Peshawar Road, Rawalpindi, Pakistan
Journal of nonlinear sciences and its applications, Tome 2 (2009) no. 2, p. 126-135.

Voir la notice de l'article provenant de la source International Scientific Research Publications

Existence of positive solution for a class of singular boundary value problems of the type
$−x''(t) = f(t, x(t), x'(t)),\quad t \in (0, 1)$
$x(0) = 0, x(1) = 0,$
is established. The nonlinearity $f \in C((0, 1) \times (0,\infty) \times (−\infty,\infty), (−\infty,\infty))$ is allowed to change sign and is singular at $t = 0, t = 1$ and/or $x = 0$. An example is included to show the applicability of our result.
DOI : 10.22436/jnsa.002.02.07
Classification : 34A45, 34B15
Keywords: Positive solutions, Singular differential equations, Dirichlet boundary conditions.

KHAN, RAHMAT ALI 1 ; ASIF, NASEER AHMAD 1

1 Centre for Advanced Mathematics and Physics, National University of Sciences and Technology, Campus of College of Electrical and Mechanical Engineering, Peshawar Road, Rawalpindi, Pakistan 
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KHAN, RAHMAT ALI; ASIF, NASEER AHMAD. POSITIVE SOLUTIONS FOR A CLASS OF SINGULAR TWO POINT BOUNDARY VALUE PROBLEMS. Journal of nonlinear sciences and its applications, Tome 2 (2009) no. 2, p. 126-135. doi : 10.22436/jnsa.002.02.07. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.002.02.07/

[1] Afrouzi, G. A.; Moghaddam, M. Khaleghy; Mohammadpour, J.; Zameni, M. On the positive and negative solutions of Laplacian BVP with Neumann boundary conditions, J. Nonlinear Sci. Appl., Volume 2 (2009), pp. 38-45

[2] Agarwal, R. P.; Regan, D. O’ Twin solutions to singular Dirichlet problems, J. Math. Anal. Appl., Volume 240 (1999), pp. 433-445

[3] Agarwal, R. P.; Regan, D. O’ An upper and lower solution approach for a generalized Thomas-Fermi theory of neutral atoms, Mathematical Problems in Engineering, Volume 8 (2002), pp. 135-142

[4] Agarwal, R. P.; O’Regan, D. Singular differential and integral equations with applications, Kluwer Academic Publishers, London, 2003

[5] Agarwal, R. P.; O’Regan, D.; Palamides, P. K. The generalized Thomas-Fermi singular boundary value problems for neutral atoms, Math. Methods in the Appl. Sci., Volume 29 (2006), pp. 49-66

[6] Berg, M. van den; Gilkey, P.; R. Seeley Heat content asymptotics with singular initial temperature distributions, J. Funct. Anal., Volume 254 (2008), pp. 3093-3122

[7] Callegari, A.; Nachman, A. A nonlinear singular boundary value problem in the theory of pseudoplastic fluids, SIAM J. Appl. Math., Volume 38 (1980), pp. 275-282

[8] Chu, J.; Franco, D. Non-collision periodic solutions of second order singular dynamical systems, J. Math. Anal. Appl., Volume 344 (2008), pp. 898-905

[9] Chu, J.; Nieto, J. J. Impulsive periodic solutions of first-order singular differential equations, Bull. London Math. Soc., Volume 40 (2008), pp. 143-150

[10] Du, X.; Zhao, Z. Existence and uniqueness of positive solutions to a class of singular m-point boundary value problems, Appl. Math. Comput., Volume 198 (2008), pp. 487-493

[11] Fenga, M.; Gea, W. Positive solutions for a class of m-point singular boundary value problems, Math. Comput. Modelling , Volume 46 (2007), pp. 375-383

[12] Janus, J.; Myjak, J. A generalized Emden-Fowler equation with a negative exponent, Nonlinear Anal., Volume 23 (1994), pp. 953-970

[13] Khan, R. A. Positive solutions of four point singular boundary value problems, Appl. Math. Comput., Volume 201 (2008), pp. 762-773

[14] Ntouyas, S. K.; Palamides, P. K. On Sturm-Liouville and Thomas-Fermi Singular Boundary Value Problems, Nonlinear Oscillations, Volume 4 (2001), pp. 326-344

[15] A. Orpel On the existence of bounded positive solutions for a class of singular BVPs, Nonlinear Anal., Volume 69 (2008), pp. 1389-1395

[16] O’Regan, D. Singular differential equations with linear and nonlinear boundary conditions, Computers Math. Appl., Volume 35 (1998), pp. 81-97

[17] Shin, J. V. A singular nonlinear differential equation arising in the Homann flow, J. Math. Anal. Appl., Volume 212 (1997), pp. 443-451

[18] Soewono, E.; Vajravelu, K.; Mohapatra, R. N. Existence and nonuniqueness of solutions of a singular nonlinear boundary layer problem, J. Math. Anal. Appl., Volume 159 (1991), pp. 251-270

[19] Yang, G. C. Existence of solutions to the third-order nonlinear differential equations arising in boundary layer theory, Appl. Math. Lett., Volume 6 (2003), pp. 827-832

[20] Yang, G. C. Positive solutions of singular Dirichlet boundary value problems with signchanging nonlinearities, Comp. Math. Appl., Volume 51 (2006), pp. 1463-1470

[21] Z. Yong Positive solutions of singular sublinear Emden-Fower boundary value problems, J. Math. Anal. Appl., Volume 185 (1994), pp. 215-222

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