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.