On a Class of Elliptic Systems in R(N)
Date
1994-09-23
Authors
Costa, David G.
Journal Title
Journal ISSN
Volume Title
Publisher
Southwest Texas State University, Department of Mathematics
Abstract
We consider a class of variational systems in ℝN of the form {−∆u + a(x)u = Fu(x, u, v) −∆v + b(x)v = F<sub>v</sub>(x, u, v), where a, b : ℝN → ℝ are continuous functions which are coercive; i.e., a(x) and b(x) approach plus infinity as x approaches plus infinity. Under appropriate growth and regularity conditions on the nonlinearities Fu(.) and Fv(.), the (weak) solutions are precisely the critical points of a related functional defined on a Hilbert space of functions u, v in H1(ℝN.
By considering a class of potentials F (x, u, v) which are nonquadratic
at infinity, we show that a weak version of the Palais-Smale condition holds true and that a nontrivial solution can be obtained by the Generalized Mountain Pass Theorem.
Our approach allows situations in which a(.) and b(.) may assume negative values, and the potential F (x, s) may grow either faster of slower than |s|2.
Description
Keywords
Quasireversibility, Final value problems, Ill-posed problems
Citation
Costa, D. G. (1994). On a class of elliptic systems in R(N). <i>Electronic Journal of Differential Equations, 1994</i>(07), pp. 1-14.
Rights
Attribution 4.0 International