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dc.contributor.authorCosta, David G. ( )
dc.identifier.citationCosta, D. G. (1994). On a class of elliptic systems in R(N). Electronic Journal of Differential Equations, 1994(07), pp. 1-14.en_US
dc.description.abstractWe consider a class of variational systems in ℝN of the form {
−∆u + a(x)u = Fu(x, u, v)
−∆v + b(x)v = Fv(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.format.extent14 pages
dc.format.medium1 file (.pdf)
dc.publisherSouthwest Texas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 1994, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectFinal value problemsen_US
dc.subjectIll-posed problemsen_US
dc.titleOn a Class of Elliptic Systems in R(N)en_US
dc.rights.licenseCreative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.



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