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

Abstract

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(; ʃ; and; u₀; are small enough.

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