Concerning positivity, cooperative elliptic and parabolic systems behave like the corresponding equations: a positive source implies that the solution is positive. Systems with a noncooperative coupling do not yield such type of behaviour. For noncooperative elliptic systems there is a restricted, but uniform, positivity result and for the non-cooperative parabolic system there is no positivity...

In this paper, we study the multiplicity of positive solutions for the Laplacian systems with sign-changing weight functions. Using the decomposition of the Nehari manifold, we prove that an elliptic system has at least two positive solutions.

In this short note we treat a 1+1-dimensional system of changing type. On different spatial domains the system is of hyperbolic and elliptic type, that is, formally, ∂2 t un − ∂2 xun = ∂tf and un−∂ xun = f on the respective spatial domains ⋃ j∈{1,...,n} ( j−1 n , 2j−1 2n ) and ⋃ j∈{1,...,n} (2j−1 2n , j n ) . We show that (un)n converges weakly to u, which solves the exponentially stable limit ...

We provide a unified proof of the asymptotics of the self-dual MaxwellChern-Simons vortices, as the Maxwell term is neglected, in both the U(1) and CP (1) case. This result is achieved by identifying and analyzing a suitable class of nonlinear elliptic systems with exponential type nonlinearities. key words: nonlinear elliptic system, Chern-Simons vortex theory MCS 2000 subject classification: ...

in this paper, we study the multiplicity of positive solutions for the laplacian systems with sign-changing weight functions. using the decomposition of the nehari manifold, we prove that an elliptic system has at least two positive solutions.

Epstein-Hubbell [6] elliptic-type integrals occur in radiation field problems. The object of the present paper is to consider a unified form of different elliptic-type integrals, defined and developed recently by several authors. We obtain asymptotic formulas for the generalized elliptic-type integrals. Keywords—Elliptic-type Integrals, Hypergeometric Functions, Asymptotic Formulas.

In [LWZ], we established Liouville-type theorems and decay estimates for solutions of a class of high order elliptic equations and systems without the boundedness assumptions on the solutions. In this paper, we continue our work in [LWZ] to investigate the role of boundedness assumption in proving Liouville-type theorems for fully nonlinear equations. We remove the boundedness assumption of sol...

In this paper we analyse semi-linear systems of partial differential equations which are motivated by the conformal formulation Einstein constraint coupled with realistic physical fields on asymptotically Euclidean (AE) manifolds. particular, electromagnetic give rise to kind system. context, under suitable conditions, prove a general existence theorem for such systems, and, in smallness assump...