Journal of Convex Analysis 25 (2018), No. 2, 421--434
Copyright Heldermann Verlag 2018
Two Positive Solutions for Superlinear Neumann Problems with a Complete Sturm-Liouville Operator
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
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.
Keywords: Neumann problem, multiple solutions, variational methods.
MSC: 34B15, 34B24, 47J30, 49J35
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