Geodesic
Two Positive Solutions for Superlinear Neumann Problems with a Complete Sturm-Liouville Operator
Journal of convex analysis, Tome 25 (2018) no. 2, pp. 421-434
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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.
Classification : 34B15, 34B24, 47J30, 49J35
Mots-clés : Neumann problem, multiple solutions, variational methods 
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     author = {G. Bonanno and A. Iannizzotto and M. Marras},
     title = {Two {Positive} {Solutions} for {Superlinear} {Neumann} {Problems} with a {Complete} {Sturm-Liouville} {Operator}},
     journal = {Journal of convex analysis},
     pages = {421--434},
     year = {2018},
     volume = {25},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JCA_2018_25_2_JCA_2018_25_2_a5/}
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G. Bonanno; A. Iannizzotto; M. Marras. Two Positive Solutions for Superlinear Neumann Problems with a Complete Sturm-Liouville Operator. Journal of convex analysis, Tome 25 (2018) no. 2, pp. 421-434. http://geodesic.mathdoc.fr/item/JCA_2018_25_2_JCA_2018_25_2_a5/