Positive solutions of an \(n\)th order three-point boundary value problem
By using the Avery-Henderson fixed point theorem and the Leggett-Williams fixed point theorem, the author investigates the multiplicity of positive solutions of the \(n\)th-order three-point boundary value problem \[ \begin{cases} y^{(n)}(t)+Q(t,y,y',\dots,y^{(n-2)})=P(t,y,y',\dots,y^{(n-1)}),\quad t\in[a,b], \\ y^{(i)}(a)=0,\quad 0\leq i\leq n-3,\\ \alpha y^{(n-2)}(\eta)+\beta y^{(n-1)}(a)=y^{(n-2)}(a),\\ \gamma y^{(n-2)}(\eta)-\delta y^{(n-1)}(b)=y^{(n-2)}(b),\end{cases} \] where \(n\geq 2\), \(a<\eta<b\), \(\delta\geq0\), \(0<\alpha<[b-\delta\eta+(\gamma-1)(a-\beta)]/(b-\eta+\beta)\), \(0<\gamma<(b-a+\delta)/(\eta-a+\beta)\), \(\beta-\alpha(b-\eta+\delta)>0\). He also presents some examples to illustrate his results.
scientific article; zbMATH DE number 6170759
scientific article