265 research outputs found
Isolated Singularities of Polyharmonic Inequalities
We study nonnegative classical solutions of the polyharmonic inequality
in a punctured neighborhood of the origin in . We give
necessary and sufficient conditions on integers and such that
these solutions satisfy a pointwise a priori bound as .Comment: 18 page
Exhaustive existence and non-existence results for some prototype polyharmonic equations in the whole space
In this paper, we are interested in entire, non-trivial, non-negative
solutions and/or entire, positive solutions to the simplest models of
polyharmonic equations with power-type nonlinearity with , , and . We aim to study the existence and non-existence
of such classical solutions to the above equations in the full range of the
constants , and . Remarkably, we are able to provide necessary
and sufficient conditions on the exponent to guarantee the existence
of such solutions in . Finally, we identify all the situations
where any entire non-trivial, non-negative classical solution must be positive.Comment: 18 pages, 0 figur
Isolated Singularities of Polyharmonic Operator in Even Dimension
We consider the equation in the sense of
distribution in where and Then it is known that solves for some non-negative constants and In
this paper we study the existence of singular solutions to in a domain is a non-negative measurable function in some Lebesgue
space. If in then we find the growth of the
nonlinearity that determines and to be In case when
we will establish regularity results when for some This paper extends the work of Soranzo
(1997) where the author finds the barrier function in higher dimensions with a specific weight function Later we discuss its
analogous generalization for the polyharmonic operator
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