Topological methods of investigation of general nonlinear elliptical boundary value problems

1984 ◽  
pp. 235-256 ◽  
Author(s):  
I. V. Skrypnik
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Topological Methods ◽  
Elliptical Boundary

scholarly journals Multiplicity results for asymmetric boundary value problems with indefinite weights

2004 ◽  
Vol 2004 (11) ◽  
pp. 957-979
Author(s):  
Francesca Dalbono
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Asymptotically Linear ◽  
Topological Methods ◽  
Multiplicity Results ◽  
Existence And Multiplicity ◽  
Rotation Numbers ◽  
Indefinite Weights ◽  
Nodal Properties

We prove existence and multiplicity of solutions, with prescribed nodal properties, to a boundary value problem of the formu″+f(t,u)=0,u(0)=u(T)=0. The nonlinearity is supposed to satisfy asymmetric, asymptotically linear assumptions involving indefinite weights. We first study some auxiliary half-linear, two-weighted problems for which an eigenvalue theory holds. Multiplicity is ensured by assumptions expressed in terms of weighted eigenvalues. The proof is developed in the framework of topological methods and is based on some relations between rotation numbers and weighted eigenvalues.

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