Exact Multiplicity of Sign‐Changing Solutions for a Class of Second‐Order Dirichlet Boundary Value Problem with Weight Function

Yulian An

Abstract and Applied Analysis, 2013, vol. 2013, issue 1

Abstract: Using bifurcation techniques and Sturm comparison theorem, we establish exact multiplicity results of sign‐changing or constant sign solutions for the boundary value problems u″ + a(t)f(u) = 0, t ∈ (0, 1), u(0) = 0, and u(1) = 0, where f ∈ C(ℝ, ℝ) satisfies f(0) = 0 and the limits f∞ = lim|s|→∞(f(s)/s), f0 = lim|s|→0(f(s)/s) ∈ {0, ∞}. Weight function a(t) ∈ C1[0, 1] satisfies a(t) > 0 on [0, 1].

Date: 2013
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https://doi.org/10.1155/2013/897307

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:897307

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