Nodal Solutions for Asymptotically Linear Second-Order BVPs on the Half-line

Original Paper


In this article, we prove under eigenvalue criteria, existence result for nodal solutions to the boundary value problem posed on the positive half-line:
$$\begin{aligned} \left\{ \begin{array}{l} -u^{\prime \prime }(t)+q(t)u(t)=u(t)f(t,u(t))\quad t>0, \\ u(0)=\lim _{t\rightarrow +\infty }u(t)=0, \end{array} \right. \end{aligned}$$
where \(q\in C\left( \mathbb {\mathbb {R} }^{+},\mathbb {\mathbb {R}}^{+}\right) \) may be unbounded from above and \( f:{\mathbb {R}}^{+}\times \mathbb {R} \rightarrow \mathbb {R} \) is a continuous function.


Sturm–Liouville BVPs on infinite intervals Linear eigenvalue problem Global bifurcation theory 

Mathematics Subject Classification

Primary 34B05 Secondary 34B40 



The authors thank the referee for all his comments and suggestions about this paper.


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Copyright information

© Iranian Mathematical Society 2018

Authors and Affiliations

  1. 1.Faculty of MathematicsUSTHBAlgiersAlgeria

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