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- Title
Multiple positive solutions for a class of Neumann problems.
- Authors
Hongliang Gao; Ruyun Ma
- Abstract
We study the existence of multiple positive solutions of the Neumann problem -u"(x) = λf (u(x)), x ∈ (0, 1), u' (0) = 0 = u' (1), where λ is a positive parameter, f ∈ C([0, ∞),ℝ) and for some β > 0 such that f (0) = 0, f (s) > 0 for s ∈ (β, ∞), f (s) < 0 for s ∈ (0, β), and θ (> β) is the unique positive zero s of F(s) = ∫s0 f (t) dt. In particular, we prove that there exist at least 2n + 1 positive solutions for λ ∈(n²π²/f'*β), ∞), where n ∈ N. The proof of our main result is based upon the bifurcation and continuation methods.
- Subjects
NEUMANN problem; BIFURCATION theory; CONTINUATION methods; DIFFERENTIAL equations; MATHEMATICAL analysis
- Publication
Electronic Journal of Qualitative Theory of Differential Equations, 2015, Issue 48-54, p1
- ISSN
1417-3875
- Publication type
Article
- DOI
10.14232/ejqtde.2015.1.48