Costa, David G.2018-08-172018-08-171994-09-23Costa, D. G. (1994). On a class of elliptic systems in R(N). <i>Electronic Journal of Differential Equations, 1994</i>(07), pp. 1-14.1072-6691https://hdl.handle.net/10877/7546We consider a class of variational systems in ℝN of the form {−∆u + a(x)u = Fu(x, u, v) −∆v + b(x)v = F_v(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.Text14 pages1 file (.pdf)enAttribution 4.0 InternationalQuasireversibilityFinal value problemsIll-posed problemsArticle