M.Sc Thesis | |

M.Sc Student | Regev Netanel |
---|---|

Subject | Criticality Theory of Half-Linear Equations with the (p,A)-Laplacian |

Department | Department of Mathematics |

Supervisor | PROFESSOR EMERITUS Yehuda Pinchover |

Let Ω be
a domain in ℝ* ^{n}*,

*Q _{A,V}*(

and its associated Euler-Lagrange equation

Q* _{ A,V}*(

where *A*
is a symmetric, measurable, locally bounded, and locally uniformly positive
definite matrix in Ω, (|∇*u*|_{A})^{2}:=<*A*(*x*)∇*u*,∇*u* >, and *V* is locally bounded in Ω.

It is assumed that *Ԛ _{A,V}* ≥0 on C

As a result, we prove further positivity properties of the functional *Q _{A,V}*
, and we generalize the Liouville-type comparison principle. Namely, given two
nonnegative functionals

Finally, we study the behavior of positive solutions of the equation Q* _{A,V}*(