On Regions of Existence and Nonexistence of solutions for a System of pp-qq-Laplacians

We give a new region of existence of solutions to the superhomogeneous Dirichlet problem \quad \begin{array}{l} -\Delta_{p} u= v^\delta\quad v>0\quad {in}\quad B,\cr -\Delta_{q} v = u^{\mu}\quad u>0\quad {in}\quad B, \cr u=v=0 \quad {on}\quad \partial B, \end{array}\leqno{(S_R)} where $B$ is the ball of radius $R>0$ centered at the origin in \RR^N. Here $\delta, \mu >0$ and $\Delta_{m} u={\rm div}(|\nabla u|^{m-2}\nabla u)$ is the $m-$Laplacian operator for $m>1$.Comment: 17 pages, accepted in Asymptotic Analysi

A noncooperative elliptic system with p-Laplacians that preserves positivity

A nonlinear noncooperative elliptic system is shown to have a positivity preserving property. That is, there exists a uniform positive constant such that, whenever the noncooperative part is bounded by this constant, positivity of the source term implies that the solution is positive. The model operator is the p-laplacian with 1 < p < # on a one-dimensional domain. The source term appears in one of the equations. 1 Introduction and main result We will study the positivity preserving property of the following nonlinear noncooperative elliptic system 8 < : -# p u (x) = f (x) - ## p (v (x)) for x ## , -# p v (x) = # p (u (x)) for x ## , u (x) = v (x) = 0 for x # ## , (1) where# = (-1, 1) . The following notation is used: # [email protected] + [email protected] The authors would like to thank Fondecyt 1940409-94, DTI, Universidad de Chile and TWI-AW, TUDelft for their support. . # p (u) = |u| p-2 u, the inverse being denoted by # inv p , . # p u ..

A comparison result for perturbed radial p-Laplacians

Consider the radially symmetric p-Laplacian for p 2 under zero Dirichlet boundary conditions. The main result of the present paper is that under appropriate conditions a solution of a perturbed (radially symmetric) p-Laplacian can be compared with the solution of the unperturbed one. As a consequence one obtains a sign preserving result for a system of p-Laplacians which are coupled in a non-quasimonotone way

Periodic solutions of periodically harvested lotka-volterra systems

We study a Lotka-Volterra system with periodic harvesting, find sufficient conditions for the existence of periodic solutions with the same period, and, under certain conditions, count the number of such periodic solutions