Mohamed Benalili & Youssef Maliki
Abstract:
We introduce a reduction method for proving the existence of
solutions to elliptic equations involving the p-Laplacian operator.
The existence of solutions is implied by the existence of a positive
essentially weak subsolution on a manifold and the existence of a
positive supersolution on each compact domain of this manifold.
The existence and nonexistence of positive supersolutions is given
by the sign of the first eigenvalue of a nonlinear operator.
Submitted March 10, 2003. Published October 21, 2003.
Math Subject Classifications: 58J05, 53C21.
Key Words: Analysis on manifolds, semi-linear elliptic PDE.
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Mohamed Benalili Universite Abou-Bakr BelKaid Faculte des Sciences Depart. Mathematiques B. P. 119, Tlemcen, Algerie email: m_benalili@mail.univ-tlemcen.dz |
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Youssef Maliki Universite Abou-Bakr BelKaid Faculte des Sciences Depart. Mathematiques B. P. 119, Tlemcen, Algerie email: malyouc@yahoo.fr |
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