Aleksander Ćwiszewski, Wojciech Kryszewski
Published 2018-06-08Version 1
In the paper the asymptotic bifurcation of solutions to a parameterized stationary semilinear Schr\"odinger equation involving a potential of the Kato-Rellich type is studied. It is shown that the bifurcation from infinity occurs if the parameter is an eigenvalue of the hamiltonian lying below the asymptotic bottom of the bounded part of the potential. Thus the bifurcating solution are related to bound states of the corresponding Schr\"odinger equation. The argument relies on the use of the (generalized) Conley index due to Rybakowski and resonance assumptions of the Landesman-Lazer or sign-condition type.
Regularity versus singularities for elliptic problems in two dimensions
The Calderón-Zygmund theory for elliptic problems with measure data
An interpolation approach to $L^{\infty}$ a priori estimates for elliptic problems with nonlinearity on the boundary
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