1,319 research outputs found
On a diffusion model with absorption and production
We discuss the structure of radial solutions of some superlinear elliptic
equations which model diffusion phenomena when both absorption and production
are present. We focus our attention on solutions defined in R (regular) or in R
\ {0} (singular) which are infinitesimal at infinity, discussing also their
asymptotic behavior. The phenomena we find are present only if absorption and
production coexist, i.e., if the reaction term changes sign. Our results are
then generalized to include the case where Hardy potentials are considered
Asymptotic analysis and sign changing bubble towers for Lane-Emden problems
We consider the semilinear Lane-Emden problem in a smooth bounded domain of
the plane. The aim of the paper is to analyze the asymptotic behavior of sign
changing solutions as the exponent p of the nonlinearity goes to infinity.
Among other results we show, under some symmetry assumptions on the domain,
that the positive and negative parts of a family of symmetric solutions
concentrate at the same point, as p goes to infinity, and the limit profile
looks like a tower of two bubbles given by a superposition of a regular and a
singular solution of the Liouville problem in the plane
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