The eigenvalue problem for thep-Laplacian-like equations
نویسندگان
چکیده
منابع مشابه
THE EIGENVALUE PROBLEM FOR THE p-LAPLACIAN-LIKE EQUATIONS
We consider the eigenvalue problem for the following p-Laplacian-like equation: −div(a(|Du| p)|Du| p−2 Du) = λf (x, u) in Ω, u = 0 on ∂Ω, where Ω ⊂ R n is a bounded smooth domain. When λ is small enough, a multiplicity result for eigen-functions are obtained. Two examples from nonlinear quantized mechanics and capillary phenomena, respectively, are given for applications of the theorems.
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and Applied Analysis 3 and using 1.9 we have ( tanpt )′ 1 − sinpt ( cospt )′ cospt 1 ∣ ∣tanpt ∣ ∣. 1.10 Like for p 2, tanpt > t for t ∈ 0, πp/2 and tanpt < t for t ∈ −πp/2, 0 , which is equivalent to ∣ ∣sinp ∣ ∣p > tΦ ( sinpt ) cospt 1.11 for t ∈ −πp/2, πp/2 , t / 0. A similar formula to 1.10 for cotp is related to the Riccati equation associated with 1.1 . Namely, if x t / 0 is a solution of 1...
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15 صفحه اولA generalized Fucik type eigenvalue problem for p-Laplacian
In this paper we study the generalized Fucik type eigenvalue for the boundary value problem of one dimensional p−Laplace type differential equations { −(φ(u′))′ = ψ(u), −T < x < T ; u(−T ) = 0, u(T ) = 0 (∗) where φ(s) = αs + − βs − , ψ(s) = λs + − μs − , p > 1. We obtain a explicit characterization of Fucik spectrum (α, β, λ, μ), i.e., for which the (*) has a nontrivial solution. (1991) AMS Su...
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ژورنال
عنوان ژورنال: International Journal of Mathematics and Mathematical Sciences
سال: 2003
ISSN: 0161-1712,1687-0425
DOI: 10.1155/s0161171203006744