Bifurcation points of Hammerstein equations
Copyright policy )Bifurcation points of Hammerstein equations
We apply global bifurcation theorems to systems of nonlinear integral equations of Hammerstein type involving a scalar parameter. To this end, we give sufficient conditions for the continuous dependence, compactness, Fréchet differentiability, and asymptotic linearity of the corresponding operators, which are more general than in the classical setting. These properties are ensured only after passing to some equivalent operator equation which typically contains fractional powers of the linear part. Finally, we show that the abstract hypotheses on the operators correspond to natural hypotheses on the kernel function and the nonlinearity in the Hammerstein equation under consideration.
- University of Würzburg Germany
Integral operators, nonlinearity in the Hammerstein equation, Equations involving nonlinear operators (general), systems of nonlinear integral equations of Hammerstein type involving a scalar parameter, Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.), fractional powers, Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones), Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), Variational problems in abstract bifurcation theory in infinite-dimensional spaces, Fréchet differentiability, asymptotic linearity, kernel function, continuous dependence, bifurcation theorems, compactness
Integral operators, nonlinearity in the Hammerstein equation, Equations involving nonlinear operators (general), systems of nonlinear integral equations of Hammerstein type involving a scalar parameter, Particular nonlinear operators (superposition, Hammerstein, Nemytskiĭ, Uryson, etc.), fractional powers, Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones), Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.), Variational problems in abstract bifurcation theory in infinite-dimensional spaces, Fréchet differentiability, asymptotic linearity, kernel function, continuous dependence, bifurcation theorems, compactness
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