| Summary: | Abstract In this paper, we consider the nonlinear eigenvalue problem u ′′′′ = λ h ( t ) f ( u ) , 0 < t < 1 , u ( 0 ) = u ( 1 ) = u ″ ( 0 ) = u ″ ( 1 ) = 0 , $$\begin{gathered} u''''= \lambda h(t)f(u),\quad 0< t< 1, \\ u(0)=u(1)=u''(0)=u''(1)=0, \\ \end{gathered} $$ where h ∈ C ( [ 0 , 1 ] , ( 0 , ∞ ) ) $h\in C([0,1], (0,\infty))$ ; f ∈ C ( R , R ) $f\in C(\mathbb{R},\mathbb{R})$ and s f ( s ) > 0 $sf(s)>0$ for s ≠ 0 $s\neq0$ , and f 0 = f ∞ = 0 $f_{0}=f_{\infty}=0$ , f 0 = lim | s | → 0 f ( s ) / s $f_{0}=\lim_{|s|\rightarrow0}f(s)/s$ , f ∞ = lim | s | → ∞ f ( s ) / s $f_{\infty}=\lim_{|s|\rightarrow\infty}f(s)/s$ . We investigate the global structure of one-sign solutions by using bifurcation techniques.
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