Eigenvalues and the One-Dimensional p-Laplacian☆☆☆
By Ravi P. Agarwal, H. Lü, Donal O'Regan. 2002
119 citations recorded by the source corpus.
We consider the boundary value problem (ϕp(u′))′ + λF(t, u) = 0, with p > 1, t ∈ (0, 1), u(0) = u(1) = 0, and with λ > 0. The value of λ is chosen so that the boundary value problem has a positive solution. In addition, we derive an explicit interval for λ such that, for any λ in this interval, the existence of a positive solution to the boundary value problem is guaranteed. In addition, the existence of two positive solutions for λ in an appropriate interval is also discussed.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/76b02312643deab3cf6a18386f7298c16144fc40
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In Applied Mathematics
In Computational Theory and Mathematics
In Mathematical Physics
Citations in the corpus
- Positive solutions to boundary value problems of p-Laplacian with fractional derivative (2017, unknown): “D(φp(D u(t))) = f (t,u(t)), 0 < t < 1, u(0) = u(1) = Du(0) = Du(1) = 0, where 1 < α ≤ 2 is a real number, D is the conformable fractional derivative, φp(s) = |s|p–2s, p > 1, φ–1 p = φq, 1/p + 1/q = 1, and f : [0, 1]× [0, +∞) → [0, +∞) is continuous.”
- On the number of positive solutions of nonlinear systems (2003, methodology): “ Tλu sup t ∈[0, 1 ] � � T i λ u(t) � �”