Saddlepoint Characterizations of Solutions to Semilinear Operator Equations |
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