Multiplicity of Positive Solutions for a Fourth-Order Quasilinear Singular Differential Equation
نویسندگان
چکیده
This paper is concerned with the multiplicity of positive solutions of boundary value problem for the fourth-order quasilinear singular differential equation (|u|u) = λg(t)f(u), 0 < t < 1, where p > 1, λ > 0. We apply the fixed point index theory and the upper and lower solutions method to investigate the multiplicity of positive solutions. We have found a threshold λ < +∞, such that if 0 < λ ≤ λ, then the problem admits at least one positive solution; while if λ > λ, then the problem has no positive solution. In particular, there exist at least two positive solutions for 0 < λ < λ.
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