Periodic-parabolic Boundary Value Problems and PositivityPresents for the first time in book form the results and techniques of such wide ranging studies as Fisher's equation of population genetics and Volterra-Lotkta systems (with diffusion) of competition and of the predator-prey type. |
Contents
Introduction | 1 |
The linear periodicparabolic eigenvalue problem | 27 |
The periodic VolterraLotka predatorprey system with diffusion | 123 |
Copyright | |
1 other sections not shown
Common terms and phrases
algebras assume asymptotically stable Banach space bifurcation bounded bu² Collège de France concave consider contradiction converges convex defined depends nontrivially Dirichlet boundary conditions dynamical systems entire orbit evolution equations exists Ə₁u F₁ Fisher's equation follows globally attractive H Brezis hence hölder implies initial conditions int(P linear logistic equation maximum principle Neumann problem Nonlinear partial differential operator parabolic partial differential equations periodic solution Poincaré map positive eigenfunction positive periodic solution positive solution principal eigenfunction principal eigenvalue proof of Theorem Proposition 2.1 prove r₁ relatively compact Remark satisfies semigroups semilinear semiorbits Similarly spr(K stable fixed point strict subequilibrium strongly order-preserving strongly order-stable strongly positive superequilibria supersolutions T-periodic Theorem 3.3 theory totally ordered trivial solution u₁ u₂ unique unstable value problem Volterra-Lotka X₁ y₁ Zorn lemma θε