Second order boundary value problems with sign-changing nonlinearities and nonhomogeneous boundary conditions

Title:

Second order boundary value problems with sign-changing nonlinearities and nonhomogeneous boundary conditions

Creator:

Graef, John R., Kong, Lingju, Kong, Qingkai, and Yang, Bo

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:f1925331-2126-4332-9ba3-04cdf7ed7b0c
uuid:f1925331-2126-4332-9ba3-04cdf7ed7b0c
doi:10.21136/MB.2011.141693

Subject:

nontrivial solutions, nonhomogeneous boundary conditions, cone, Krein-Rutman theorem, and Leray-Schauder degree

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

The authors consider the boundary value problem with a two-parameter nonhomogeneous multi-point boundary condition u ′′ + g(t)f(t, u) = 0, t ∈ (0, 1), u(0) = αu(ξ) + λ, u(1) = βu(η) + µ. Criteria for the existence of nontrivial solutions of the problem are established. The nonlinear term f(t, x) may take negative values and may be unbounded from below. Conditions are determined by the relationship between the behavior of f(t, x)/x for x near 0 and ±∞, and the smallest positive characteristic value of an associated linear integral operator. The analysis mainly relies on topological degree theory. This work complements some recent results in the literature. The results are illustrated with examples.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

337-356

Source:

Mathematica bohemica | 2011 Volume:136 | Number:4

Harvested from:

CDK

Metadata only:

false