Electronic Journal of Qualitative Theory of Differential Equations (Oct 2009)

Positive solutions for singular $\phi-$Laplacian BVPs on the positive half-line

  • Smail Djebali,
  • O. Saifi

DOI
https://doi.org/10.14232/ejqtde.2009.1.56
Journal volume & issue
Vol. 2009, no. 56
pp. 1 – 24

Abstract

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In this work, we are concerned with the existence of positive solutions for a $\phi$ Laplacian boundary value problem on the half-line. The results are proved using the fixed point index theory on cones of Banach spaces and the upper and lower solution technique. The nonlinearity may exhibit a singularity at the origin with respect to the solution. This singularity is treated by regularization and approximation together with compactness and sequential arguments.