Abstract
The solvability of one dimensional fourth-order p-Laplace equations of the type \(\left\{ \begin{gathered} \left( {g\left( {u\prime \prime } \right)} \right)\prime \prime + \lambda a\left( t \right)u = 0,{\text{ }}0 < t < 1, \hfill \\ u\left( 0 \right) = u\left( 1 \right) = u\prime \prime \left( 0 \right) = u\prime \prime \left( 1 \right) = 0, \hfill \\ \end{gathered} \right.\), where, g(v) ≔ | v |p−2 v, p > 1 is investigated. With cone compression/extension theorem, some existence and multiplicity results of positive solution have been required according to different growth condition of nonlinear form f at zero and at infinity.
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Bai, Zb. Existence and Multiplicity of Positive Solutions for a Fourth-Order P-Laplace Equations. Applied Mathematics and Mechanics 22, 1476–1480 (2001). https://doi.org/10.1023/A:1022851213931
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DOI: https://doi.org/10.1023/A:1022851213931