On Elliptic Equations in RN with Critical Exponents

Alves, C. O.Goncalves, J. V.Miyagaki, Olimpio H.2018-08-242018-08-241996-10-22Alves, C. O., Goncalves, J. V., & Miyagaki, O. H. (1996). On elliptical equations in RN with critical exponents. <i>Electronic Journal of Differential Equations, 1996</i>(09), pp. 1-11.1072-6691https://hdl.handle.net/10877/7609In this note we use variational arguments –namely Ekeland’s Principle and the Mountain Pass Theorem– to study the equation −∆u + α(x)u = λuq + u2*−1 in ℝN. The main concern is overcoming compactness difficulties due both to the unboundedness of the domain ℝN, and the presence of the critical exponent 2* = 2N / (N − 2).Text11 pages1 file (.pdf)enAttribution 4.0 InternationalElliptic equationsUnbounded domainsCritical exponentsVariational methodsOn Elliptic Equations in RN with Critical ExponentsArticleThis work is licensed under a Creative Commons Attribution 4.0 International License.