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Multiple critical points for near-symmetric functionals and application to a non-homogenous boundary value problem

University of British Columbia

A method of perturbation from symmetry, developed by Bolle [Bol99] in order to prove that a particular non-homogeneous boundary value problem has infinitely many solutions, is presented as an abstract result in critical point theory. The main theorem establishes the existence of multiple critical points for certain "near-symmetric" functionals. As an application, we consider the problem [mathematical problem shown in abstract] where Ω is a smooth, bounded, open subset of ⁿ (n > 2), λ > 0,1 < q < p, f ε C(Ω, R) and uo ε C²(<მΩ, R). We prove that this equation has an infinite number of solutions for P < (n+1)/(n-1) and that for any sub-crtical p i.e., p < (n+2)/(n-2), there are as many solutions as we like, provided ʃ and u₀ are small enough.

Thesis/Dissertation

application/pdf

2009-07-09

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http://hdl.handle.net/2429/10544

Mathematics

University of British Columbia

UBCV

DSpace