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https://doi.org/10.3336/gm.46.1.14

Variational characterisation of nodal solutions of a Sturm-Liouville problem with strong nonlinearity

Lavoslav Čaklović ; Faculty of Natural Sciences, Department of Mathematics, University of Zagreb, 10000 Zagreb, Croatia

Sažetak

We consider sublinear Sturm-Liouville problem

-u''+ψ(t) |u |p-1 u =λ u, p>1,
u(0)=u(1)=0

where ψ is positive and continuous. Using the Nehari variational technique and critical point theory we prove that for each nN there is unique (up to the sign) n-nodal solution of the b.v.p. which is the critical point of a restricted functional associated to the problem.

Ključne riječi

Critical point theory; Palais-Smale condition; Sturm-Liouville problem; nodal solutions

Hrčak ID:

68893

URI

https://hrcak.srce.hr/68893

Datum izdavanja:

13.6.2011.

Posjeta: 1.042 *