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- Title
UNILATERAL GLOBAL INTERVAL BIFURCATION FOR KIRCHHOFF TYPE PROBLEMS AND ITS APPLICATIONS.
- Authors
Shen, Wenguo
- Abstract
In this paper, we establish a unilateral global bifurcation result from interval for a class of Kirchhoff type problems with nondifferentiable nonlinearity. By applying the above result, we shall prove the existence of one-sign solutions for the following Kirchhoff type problems. {-M(∫Ω |∇u|2 dx)Δu = α(x)u+ + β(x)u- + ra(x)f(u), in Ω, u = 0; on ∂Ω, where Ω is a bounded domain in ℝN with a smooth boundary ∂Ω, M is a continuous function, r is a parameter, a(x) ∈ C(Ω¯) is positive, u+ = max{u, 0}, u- = -min{u, 0}, α, β ∈ C(Ω¯), f ∈ C(ℝ,ℝ), sf(s) > 0 for s ∈ ℝ+, and f0 ∈ (0,∞) and f∞ ∈ (0,∞] or f0 = ∞ and f∞ ∈ [0,∞], where f0 = lim|s| → 0 f(s)/s, f∞ = lim|s| → + ∞ f(s)/s. We use unilateral global bifurcation techniques and the approximation of connected components to prove our main results.
- Subjects
BIFURCATION theory; NONLINEAR theories; CONTINUOUS functions; NONDIFFERENTIABLE functions; APPROXIMATION theory
- Publication
Communications on Pure & Applied Analysis, 2018, Vol 17, Issue 1, p21
- ISSN
1534-0392
- Publication type
Article
- DOI
10.3934/cpaa.2018002