Bifurcation from infinity and higher order ordinary differential equations (Q1909983)

The purpose of the paper is to obtain existence results for classes of \(n\)th order boundary value problems for ordinary differential equations: \(Ly(x)- \lambda_1(- 1)^{n- k} p(x) y(x)+ g(y(x))= h(x)\), \(a\leq x\leq b\), \(y^{(j)}(a)= 0\), \(j= 0,\dots, k- 1\), \(y^{(j)}(b)= 0\), \(j= 0,\dots, n- k- 1\), where \(k\in \{1, \dots, n- 1\}\) and \(Ly(x)= y^{(n)}+ a_{n- 1}(x) y^{(n- 1)}+\cdots+ a_0(x) y\). The authors rely on an abstract result concerning bifurcation from infinity to obtain continua of large positive or negative solutions.