Eugenio
Massa*, An Existence Result for a Linear-Superlinar Elliptic
System with Neumann Boundary Conditions*

Abstract

In this work, we consider an elliptic system of two equations in dimension one (with Neumann boundary conditions) where the nonlinearities are asymptotically linear at $-\infty$ and superlinear at $+\infty$. We obtain that, under suitable hypotheses, a solution exists for any couple of forcing terms in $L^2$ .

We also present a similar result in which the superlinearity is in only one of the two equations, and we discuss the resonant problem too.

Key words and phrases: Elliptic systems, linear-superlinear problems, Galerkin approximation

1991 Mathematical Subject Classification: 35J55 (49J35)

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In this work, we consider an elliptic system of two equations in dimension one (with Neumann boundary conditions) where the nonlinearities are asymptotically linear at $-\infty$ and superlinear at $+\infty$. We obtain that, under suitable hypotheses, a solution exists for any couple of forcing terms in $L^2$ .

We also present a similar result in which the superlinearity is in only one of the two equations, and we discuss the resonant problem too.

Key words and phrases: Elliptic systems, linear-superlinear problems, Galerkin approximation

1991 Mathematical Subject Classification: 35J55 (49J35)

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December 13, 2004