ISSN:
1573-2878
Keywords:
Positive solutions
;
lattice fixed-point theorem
;
sublinearity
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract The nonlinear initial-value problemu″(t)+f(t,u(t))=0,u(t 0)+bu′(t 0)=c,t 0≥0,b≤0,c≥0, is considered for positive solutions on [t 0, ∞). Existence of positive solutions is proved without the hypothesis thatf(t, ω)≥0 (or ≤0), using the lattice fixed point theorem. A monotonicity condition inf(t, ω) is used to prove the uniqueness of the solution of the initial-value problem. Whenf(t, ω)≥0 (or ≤0), uniqueness is also obtained under a sublinearity condition onf(t, ω).
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00934602
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