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Infinitely Many Sign‐Changing Solutions for Some Nonlinear Fourth‐Order Beam Equations

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  • Ying Wu
  • Guodong Han

Abstract

Several new existence theorems on positive, negative, and sign‐changing solutions for the following fourth‐order beam equation are obtained: u(4) = f(t, u(t)), t ∈ [0, 1]; u(0) = u(1) = u′′(0) = u′′(1) = 0, where f ∈ C([0, 1] × ℝ1, ℝ1). In particular, an infinitely many sign changing solution theorem is established. The method of the invariant set of decreasing flow is employed to discuss this problem.

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Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:635265
DOI: 10.1155/2013/635265
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