Bifurcation of nodal solutions for the Moore-Nehari differential equation
This paper deals with the bifurcation of nodal solutions for the Moore-Nehari differential equation. If a solution of the equation is odd or even, it is said to be symmetric. For a non-negative integer \(n\), a solution is called an \(n\)-nodal solution if it has exactly \(n\) zeros in the given interval. If the solution is \(n\)-nodal and symmetric, it is called \(n\)-nodal symmetric. The author proves that the equation has a unique \(n\)-nodal symmetric solution \(u_{n}\left( x,\lambda\right).\) The author also shows that the curve \(\left( \lambda,u_{2n+1}\left(x,\lambda\right) \right) \) of odd solutions does not bifurcate, but the curve \(\left( \lambda,u_{2n}\left( x,\lambda\right) \right) \) of even solutions, which is an \(n\)-nodal asymmetric solution, bifurcates.
scientific article; zbMATH DE number 7630742
scientific article