Abstract
Multiple solutions for Kirchhoff type problems involving super-linear and sub-linear terms
Highlights
This paper concerns the multiplicity of solutions for the following Kirchhoff type problem
Kirchhoff type problems were proposed by Kirchhoff in 1883 [14] as an extension of the classical D’Alembert’s wave equation for free vibration of elastic strings
It is related to the stationary analogue of the equation utt − (a + b Ω |∇u|2dx) u = h(x, u) in Ω, (1.2)
Summary
This paper concerns the multiplicity of solutions for the following Kirchhoff type problem +∞, they proved that there exists λ0 > 0 such that for any λ ∈ [0, λ0), (1.5) has at least one positive solution. Assume that in the problem (1.1), f (u) = |u|p−2u with 2 < p < 6 and g(x) is a nonnegative function with the following property: (g1)
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