## Abstract and Applied Analysis

### Multiplicity results for asymmetric boundary value problems with indefinite weights

Francesca Dalbono

#### Abstract

We prove existence and multiplicity of solutions, with prescribed nodal properties, to a boundary value problem of the form $u''+f(t,u)=0$, $u(0)=u(T)=0$. 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2004, Number 11 (2004), 957-979.

Dates
First available in Project Euclid: 30 December 2004

https://projecteuclid.org/euclid.aaa/1104418104

Digital Object Identifier
doi:10.1155/S108533750440102X

Mathematical Reviews number (MathSciNet)
MR2130222

Zentralblatt MATH identifier
1079.34007

Subjects
Primary: 34B15: Nonlinear boundary value problems

#### Citation

Dalbono, Francesca. Multiplicity results for asymmetric boundary value problems with indefinite weights. Abstr. Appl. Anal. 2004 (2004), no. 11, 957--979. doi:10.1155/S108533750440102X. https://projecteuclid.org/euclid.aaa/1104418104