The existence of solutions to Sturm-Liouville boundary value problems with Laplacian-like operator.
Writing the nonlinear differential equation \((\phi(u^\prime))^\prime+f(t,u,u^\prime)=0\) on \([0,T]\) with mixed boundary conditions at either endpoint, where \(\phi\) is strictly increasing with \(y\phi(y)>0\) for \(y\neq 0\) and \(| \phi(y)| /| y| ^\alpha\) and \(f(t,u,u^\prime)/\phi(u)\) are bounded and bounded away from zero, in terms of generalized polar coordinates, results are obtained on the period of any closed trajectory and the number of solutions.
scientific article; zbMATH DE number 1885878