## Saddlepoint Characterizations of Solutions to Semilinear Operator Equations |

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### 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 anti-monotone Banach space boundary value problems Chapter concave condition LL2 condition N3 convex analysis convex functional corresponding critical point decomposition of H defined Definition double-sided resonance eigenspace eigenvalues elliptic boundary value exists F[xk(wk finite-dimensional Fk[uk(wk Gateaux Gateaux derivatives Hilbert space inequality interact k—oo Landesman Lazer Lemma lim Fm[um(wm linear growth restriction linear operator max inf F(x max max inf max min sup Mitchell 14 monotonicity condition Nm(um nonlinear term normed vector space obtain a solution one-sided resonance point of F Proof of Claim Proposition 3.4 require saddle Saddlepoint Characterizations saddlepoint reduction method saddlepoint solution self-adjoint operator semilinear elliptic boundary sequence of solutions spectral gap strictly convex strongly monotone subset subspaces sup F(x Suppose Theorem unbounded operators variational characterization VF(x weak solution xk(wk xm(wm y(wk y(wm yk(wk yk{wk ym(wm ym{wm