On a Class of Elliptic Systems in R(N)
| dc.contributor.author | Costa, David G. | |
| dc.date.accessioned | 2018-08-17T17:19:38Z | |
| dc.date.available | 2018-08-17T17:19:38Z | |
| dc.date.issued | 1994-09-23 | |
| dc.description.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. | |
| dc.description.department | Mathematics | |
| dc.format | Text | |
| dc.format.extent | 14 pages | |
| dc.format.medium | 1 file (.pdf) | |
| dc.identifier.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. | |
| dc.identifier.issn | 1072-6691 | |
| dc.identifier.uri | https://hdl.handle.net/10877/7546 | |
| dc.language.iso | en | |
| dc.publisher | Southwest Texas State University, Department of Mathematics | |
| dc.rights | Attribution 4.0 International | |
| dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | |
| dc.source | Electronic Journal of Differential Equations, 1994, San Marcos, Texas: Southwest Texas State University and University of North Texas. | |
| dc.subject | Quasireversibility | |
| dc.subject | Final value problems | |
| dc.subject | Ill-posed problems | |
| dc.title | On a Class of Elliptic Systems in R(N) | |
| dc.type | Article |