Bifurcation of Gradient Mappings Possessing the Palais-Smale Condition | Zendy

Elliot Tonkes | Zendy

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Bifurcation of Gradient Mappings Possessing the Palais-Smale Condition

Author(s) -

Elliot Tonkes

Publication year - 2011

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/2011/564930

Subject(s) - mathematics , bifurcation , sobolev space , mathematical analysis , eigenvalues and eigenvectors , nonlinear system , class (philosophy) , operator (biology) , exponent , pure mathematics , physics , biochemistry , chemistry , linguistics , philosophy , repressor , quantum mechanics , artificial intelligence , computer science , transcription factor , gene

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

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