Bifurcation of Gradient Mappings Possessing the Palais-Smale Condition. (2nd May 2011)

• Record Type: Journal Article
• Authors: Tonkes, Elliot
• Other Names: Squassina Marco Academic Editor.
• Is Part Of: International journal of mathematics and mathematical sciences. Volume 2011(2011)
• Publication Date: 2011-05-02
• Subjects: Mathematics -- Periodicals; 510.5
• DOI: 10.1155/2011/564930
• Languages: English
• ISSNs: 0161-1712

Abstract

Abstract : This paper considers bifurcation at the principal eigenvalue of a class of gradient operators which possess the Palais-Smale condition. The existence of the bifurcation branch and the asymptotic nature of the bifurcation is verified by using the compactness in the Palais Smale condition and the order of the nonlinearity in the operator. The main result is applied to estimate the asyptotic behaviour of solutions to a class of semilinear elliptic equations with a critical Sobolev exponent.