729 research outputs found
Some recent results on singular p-Laplacian equations
A short account of some recent existence, multiplicity, and uniqueness results for singular p-Laplacian problems either in bounded domains or in the whole space is performed, with a special attention to the case of convective reactions. An extensive bibliography is also provided
On explosive solutions for a class of quasi-linear elliptic equations
We study existence, uniqueness, multiplicity and symmetry of large solutions
for a class of quasi-linear elliptic equations. Furthermore, we characterize
the boundary blow-up rate of solutions, including the case where the
contribution of boundary curvature appears.Comment: 34 page
Functional Inequalities: New Perspectives and New Applications
This book is not meant to be another compendium of select inequalities, nor
does it claim to contain the latest or the slickest ways of proving them. This
project is rather an attempt at describing how most functional inequalities are
not merely the byproduct of ingenious guess work by a few wizards among us, but
are often manifestations of certain natural mathematical structures and
physical phenomena. Our main goal here is to show how this point of view leads
to "systematic" approaches for not just proving the most basic functional
inequalities, but also for understanding and improving them, and for devising
new ones - sometimes at will, and often on demand.Comment: 17 pages; contact Nassif Ghoussoub (nassif @ math.ubc.ca) for a
pre-publication pdf cop
Shooting with degree theory: Analysis of some weighted poly-harmonic systems
In this paper, the author establishes the existence of positive entire
solutions to a general class of semilinear poly-harmonic systems, which
includes equations and systems of the weighted Hardy--Littlewood--Sobolev type.
The novel method used implements the classical shooting method enhanced by
topological degree theory. The key steps of the method are to first construct a
target map which aims the shooting method and the non-degeneracy conditions
guarantee the continuity of this map. With the continuity of the target map, a
topological argument is used to show the existence of zeros of the target map.
The existence of zeros of the map along with a non-existence theorem for the
corresponding Navier boundary value problem imply the existence of positive
solutions for the class of poly-harmonic systems.Comment: 19 pages, author's accepted version including corrections to a few
typographical error
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