Abstract

We establish existence of two positive solutions for a nonlinear Sturm-Liouville equation in a complete form, that is, involving the first derivative, with Neumann boundary conditions. The conclusion is obtained by assuming a suitable behaviour of the nonlinearity in a well determined interval and at infinity, requiring no condition at zero. Our approach is based on variational methods.

Author information

Contact details are reproduced from the original publication and may be historical.

Gabriele Bonanno

Dept. of Engineering, University of Messina, C.da Di Dio - Sant'Agata, 98166 Messina, Italy

bonanno@unime.it

Antonio Iannizzotto

Dept. of Mathematics and Computer Science, University of Cagliari, Viale L. Merello 92, 09123 Cagliari, Italy

antonio.iannizzotto@unica.it

Monica Marras

Dept. of Mathematics and Computer Science, University of Cagliari, Viale L. Merello 92, 09123 Cagliari, Italy

mmarras@unica.it

Keywords

  • Neumann problem
  • multiple solutions
  • variational methods

Mathematics Subject Classification

34B15, 34B24, 47J30, 49J35

Suggested citation

G. Bonanno, A. Iannizzotto, M. Marras. “Two Positive Solutions for Superlinear Neumann Problems with a Complete Sturm-Liouville Operator.” Journal of Convex Analysis 25 (2018), No. 2, 421–434.

Copyright Heldermann Verlag 2018