Electron. J. Diff. Equ., Vol. 2013 (2013), No. 73, pp. 1-18.

Singular boundary-value problems with variable coefficients on the positive half-line

Smail Djebali, Ouiza saifi, Samira Zahar

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.

Show me the PDF file (276 KB), TEX file, and other files for this article.

Smaïl Djebali
Laboratoire "Théorie du Point Fixe et Applications"
École Normale Supéerieure, Kouba
B.P. 92, 16050 Kouba. Algiers, Algeria
email: djebali@ens-kouba.dz, djebali@hotmail.com
  Ouiza Saifi
Department of Economics, Faculty of Economic and Management Sciences
Algiers University 3, Algeria
email: saifi_kouba@yahoo.fr
  Samira Zahar
Department of Mathematics
A.E. Mira University, 06000. Bejaia, Algeria
email: zahar_samira@yahoo.fr

Return to the EJDE web page