Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 73, pp. 1-18.

Title: Singular boundary-value problems with variable coefficients on
       the positive half-line
        
Authors: Smail Djebali (Ecole Normale Superieure, Algiers, Algeria)
         Ouiza saifi  (Algiers Univ. 3, Algeria)
         Samira Zahar (A.E. Mira Univ., Bejaia, Algeria

Abstract:
 This work  concerns the existence and the multiplicity
 of solutions for singular boundary-value problems with a
 variable coefficient, posed on the positive half-line.
 When the nonlinearity is positive but may have a space singularity
 at the origin, the existence of single and twin positive solutions is
 obtained by means of the fixed point index theory.
 The singularity is treated by approximating the nonlinearity,
 which is assumed to satisfy general growth conditions.
 When the nonlinearity is not necessarily positive, the Schauder fixed
 point theorem is combined with the method of upper and lower solutions
 on unbounded domains to prove existence of solutions.
 Our results extend those in [18] and are illustrated
 with examples.

Submitted July 22, 2012. Published March 17, 2013.
Math Subject Classifications: 34B15, 34B18, 34B40.
Key Words: Positive solution; variable coefficient; 
           lower and upper solutions; singular problem; half-line;
           multiplicity; uniqueness; fixed point index.