Multiplicity results for a fourth-order boundary value problem. (English) Zbl 0836.73032

Summary: This paper deals with multiplicity results for nonlinear elastic equations of the type \(y^{(IV)} - \alpha_1y + \beta_1y'' + g(x,y,y'') = e\), \(0 < x < 1\), \(y(0) = y''(0) = y'(1) = y'''(1) = 0\), where \(e \in L^2 (0,1)\), \(g : [0,1] \times \mathbb{R} \times \mathbb{R} \to \mathbb{R}\) is a bounded continuous function, and the pair \((\alpha_1, \beta_1)\) satisfies the conditions \(\alpha_1 + (0 + 0.5)^2 \pi^2 \beta_1 = (0 + 0.5)^4 \pi^4\) and \(\alpha_1 + (k + 0.5)^2 \pi^2 \beta_1 \neq (k + 0.5)^4 \pi^4\) for all \(k \in N\).


74K10 Rods (beams, columns, shafts, arches, rings, etc.)
34B15 Nonlinear boundary value problems for ordinary differential equations
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