Glasnik matematički, Vol. 46 No. 1, 2011.
Izvorni znanstveni članak
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
Datum izdavanja:
13.6.2011.
Posjeta: 1.381 *