Boundary value problems of Sturm-Liouville and periodic type for the second order nonlinear ODE u'' + λ f (t, u) = 0 are considered. Multiplicity results are obtained, for λ positive and large, under suitable growth restrictions on f (t, u) of superlinear type at u = 0 and of sublinear type at u = ∞. Only one-sided growth conditions are required. Applications are given to the equation u'' + λq(t)f(u) = 0, allowing also a weight function q(t) of nonconstant sign.
Pairs of nodal solutions for a class of nonlinear problems with one-sided growth conditions
BOSCAGGIN, Alberto;
2013-01-01
Abstract
Boundary value problems of Sturm-Liouville and periodic type for the second order nonlinear ODE u'' + λ f (t, u) = 0 are considered. Multiplicity results are obtained, for λ positive and large, under suitable growth restrictions on f (t, u) of superlinear type at u = 0 and of sublinear type at u = ∞. Only one-sided growth conditions are required. Applications are given to the equation u'' + λq(t)f(u) = 0, allowing also a weight function q(t) of nonconstant sign.
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