779 research outputs found
A new critical curve for a class of quasilinear elliptic systems
We study a class of systems of quasilinear differential inequalities
associated to weakly coercive differential operators and power reaction terms.
The main model cases are given by the -Laplacian operator as well as the
mean curvature operator in non parametric form. We prove that if the exponents
lie under a certain curve, then the system has only the trivial solution. These
results hold without any restriction provided the possible solutions are more
regular. The underlying framework is the classical Euclidean case as well as
the Carnot groups setting.Comment: 28 page
Nonexistence of positive supersolutions of elliptic equations via the maximum principle
We introduce a new method for proving the nonexistence of positive
supersolutions of elliptic inequalities in unbounded domains of .
The simplicity and robustness of our maximum principle-based argument provides
for its applicability to many elliptic inequalities and systems, including
quasilinear operators such as the -Laplacian, and nondivergence form fully
nonlinear operators such as Bellman-Isaacs operators. Our method gives new and
optimal results in terms of the nonlinear functions appearing in the
inequalities, and applies to inequalities holding in the whole space as well as
exterior domains and cone-like domains.Comment: revised version, 32 page
Entire solutions of quasilinear elliptic systems on Carnot Groups
We prove general a priori estimates of solutions of a class of quasilinear
elliptic system on Carnot groups. As a consequence, we obtain several non
existence theorems. The results are new even in the Euclidean setting.Comment: 21 pages submitte
A priori estimates for some elliptic equations involving the -Laplacian
We consider the Dirichlet problem for positive solutions of the equation
in a convex, bounded, smooth domain , with locally Lipschitz continuous. \par We provide sufficient
conditions guarantying a priori bounds for positive solutions of
some elliptic equations involving the -Laplacian and extend the class of
known nonlinearities for which the solutions are a priori
bounded. As a consequence we prove the existence of positive solutions in
convex bounded domains
Noether Symmetries and Critical Exponents
We show that all Lie point symmetries of various classes of nonlinear
differential equations involving critical nonlinearities are
variational/divergence symmetries.Comment: Published in SIGMA (Symmetry, Integrability and Geometry: Methods and
Applications) at http://www.emis.de/journals/SIGMA
Asymptotic and optimal Liouville properties for Wolff type integral systems
This article examines the properties of positive solutions to fully nonlinear
systems of integral equations involving Hardy and Wolff potentials. The first
part of the paper establishes an optimal existence result and a Liouville type
theorem for the integral systems. Then, the second part examines the decay
rates of positive bound states at infinity. In particular, a complete
characterization of the asymptotic properties of bounded and decaying solutions
is given by showing that such solutions vanish at infinity with two principle
rates: the slow decay rates and the fast decay rates. In fact, the two rates
can be fully distinguished by an integrability criterion. As an application,
the results are shown to carry over to certain systems of quasilinear
equations.Comment: 28 pages, author's final version incorporating reviewer comments and
suggestion
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