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Bifurcation techniques for Lidstone boundary value problems. (English) Zbl 1140.34321
Summary: By employing bifurcation techniques, this paper investigates the existence of nontrivial solutions (single and multiple) for Lidstone boundary value problems $$\cases (-1)^n u^{(2n)}(t)=f(t,u(t),u''(t),\dots,u^{(2(n-1))}(t)),\quad & t\in (0,1);\\ u^{(2i)}(0)=u^{(2i)}(1)=0, & i=0,1,\dots,n-1.\endcases$$ Our results improve on those in the literature.

MSC:
34B15Nonlinear boundary value problems for ODE
34C23Bifurcation (ODE)
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References:
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