Three positive solutions for one-dimensional p-Laplacian problem with sign-changing weight
نویسندگان
چکیده
منابع مشابه
Multiplicity of Positive Solutions of laplacian systems with sign-changing weight functions
In this paper, we study the multiplicity of positive solutions for the Laplacian systems with sign-changing weight functions. Using the decomposition of the Nehari manifold, we prove that an elliptic system has at least two positive solutions.
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We consider the system ⎧ ⎨ ⎩ −Δ p u = λF (x, u, v), x ∈ Ω, −Δ q v = λH(x, u, v), x ∈ Ω, u = 0 = v, x ∈ ∂Ω, where F (x, u, v) = [g(x)a(u) + f (v)], H(x, u, v) = [g(x)b(v) + h(u)], Ω is a bounded domain in R N (N ≥ 1) with smooth boundary ∂Ω, λ is a real positive parameter and Δ s z = div (|∇z| s−2 ∇z), s > 1, (s = p, q) is a s-laplacian operator. Here g is a C 1 sign-changing function that may b...
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A p-Laplacian system with Dirichlet boundary conditions is investigated. By analysis of the relationship between the Nehari manifold and fibering maps, we will show how the Nehari manifold changes as λ,μ varies and try to establish the existence of multiple positive solutions. c © 2007 Elsevier Ltd. All rights reserved.
متن کاملmultiplicity of positive solutions of laplacian systems with sign-changing weight functions
in this paper, we study the multiplicity of positive solutions for the laplacian systems with sign-changing weight functions. using the decomposition of the nehari manifold, we prove that an elliptic system has at least two positive solutions.
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We prove the existence of three monotone positive solutions for the second-order multi-point boundary value problem, with sign changing coefficients, [p(t)φ(x′(t))]′ + f(t, x(t), x′(t)) = 0, t ∈ (0, 1), x′(0) = − l X i=1 aix (ξi) + m X i=l+1 aix (ξi), x(1) + βx′(1) = k X i=1 bix(ξi)− m X i=k+1 bix(ξi)− m X i=1 cix (ξi). To obtain these results, we use a fixed point theorem for cones in Banach s...
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ژورنال
عنوان ژورنال: Applied Mathematics Letters
سال: 2015
ISSN: 0893-9659
DOI: 10.1016/j.aml.2015.04.007