Saddlepoint Characterizations of Solutions to Semilinear Operator Equations |
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Page 3
... Amann [ 1 ] and Bates [ 2 ] where the direct sum decomposition was extended to three spaces and the problem of finding critical points of the functional ( 1.1 ) was reduced to a similar problem in the ( finite - dimensional ) resonant ...
... Amann [ 1 ] and Bates [ 2 ] where the direct sum decomposition was extended to three spaces and the problem of finding critical points of the functional ( 1.1 ) was reduced to a similar problem in the ( finite - dimensional ) resonant ...
Page 18
... Amann [ 1 ] , Mitchell [ 14 ] , Castro and Lazer [ 5 ] , Castro [ 4 ] , Landesman , Lazer and Meyers [ 13 ] , Ward [ 21 ] , and Shapiro [ 18 ] . The particular approach taken here is most similar to the one developed in Amann [ 1 ] and ...
... Amann [ 1 ] , Mitchell [ 14 ] , Castro and Lazer [ 5 ] , Castro [ 4 ] , Landesman , Lazer and Meyers [ 13 ] , Ward [ 21 ] , and Shapiro [ 18 ] . The particular approach taken here is most similar to the one developed in Amann [ 1 ] and ...
Page 23
... Amann [ 1 ] , and are also used by Mitchell [ 14 ] . We are now ready to state and prove a modified version of a theorem first proved in [ 14 ] . Theorem 1. Let L satisfy conditions ( L1 ) and ( L2 ) , and let N satisfy conditions ( N1 ) ...
... Amann [ 1 ] , and are also used by Mitchell [ 14 ] . We are now ready to state and prove a modified version of a theorem first proved in [ 14 ] . Theorem 1. Let L satisfy conditions ( L1 ) and ( L2 ) , and let N satisfy conditions ( N1 ) ...
Contents
Preliminary Functional Analysis and Operator Theory | 6 |
Preliminary Convex Analysis | 13 |
The Saddlepoint Reduction | 18 |
6 other sections not shown
Common terms and phrases
Amann anti-coercive boundary value problems bounded operator Chapter Conditions L1 convex analysis convex functional critical point defined Definition differentiable double-sided resonance eigenspace eigenvalues elliptic boundary value exists F[xk(wk finite-dimensional Fréchet derivative Gâteaux derivatives Gâteaux differentiable H₁ Hilbert space hypotheses L²(N Landesman Lazer Lemma linear growth restriction linear operator Lu(w max inf F(x max max inf max min sup Mitchell 14 N₁ nonlinear term normed vector space obtain a solution one-sided resonance orthogonal point of F properties Proposition 3.4 require saddle saddlepoint reduction method saddlepoint solution self-adjoint operator Semilinear Operator Equations spectral gap spectrum strictly convex strongly monotone subspaces sup F(x Theorem Uk wk uk(wk um(wm variational characterization VF(u weak solution x(wk x(wn X₁ xk wk xk(wk xm(wm y(wk y(wm y(wn y(wo Y₁ yk wk yk(wk Ym Wm Ym(Wm