Glasnik Matematicki, Vol. 46, No.1 (2011), 167-188.

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
e-mail: caklovic@math.hr


Abstract.   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 ninN 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.

2000 Mathematics Subject Classification.   34C25, 47H15, 58E05, 58F05, 70H30.

Key words and phrases.   Critical point theory, Palais-Smale condition, Sturm-Liouville problem, nodal solutions.


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DOI: 10.3336/gm.46.1.14


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