Solutions for 2nth order lidstone BVP on time scales
In this paper, we prove the existence of solutions for nonlinear Lidstone boundary value problems by using the monotone method on time scale and also we show the existence of at least one positive solution if f is either superlinear or sublinear by the fixed point theorem in a Banach space.
Anahtar Kelimeler:
Lidstone boundary value problem, upper and lower solutions, fixed point theorem, positive solution.
Solutions for 2nth order lidstone BVP on time scales
In this paper, we prove the existence of solutions for nonlinear Lidstone boundary value problems by using the monotone method on time scale and also we show the existence of at least one positive solution if f is either superlinear or sublinear by the fixed point theorem in a Banach space.
Keywords:
Lidstone boundary value problem, upper and lower solutions, fixed point theorem, positive solution.,
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- for 0≤ r ≤ r2and hence, for y∈ P and y = r2, we have T y(t) = (−1)nG(t, s)f(s, yσ(s)y (s), ..., y (n−1) (s)) s ≤ σ(1) (−1)nGn(t, s)g(r2) s ≤ ηr2 (−1)G s ≤ ηr2 σ(1) ≤ r2= y , and again we hence T y ≤ y for y ∈ P ∩ ∂Ω2, where Ω2={y ∈ B : y ≤ r2} in both cases. It follows from part (ii) of Theorem 3.1 that T has a Şxed point in P∩ (Ω2\Ω1) and this implies that our given LBVP (1.1), (1.2) has a positive solution.
- ISSN: 1300-0098
- Yayın Aralığı: Yılda 6 Sayı
- Yayıncı: TÜBİTAK
Sayıdaki Diğer Makaleler
A perturbation of m-order derivations on Banach algebras
C1 modules with respect to a hereditary torsion theory
Solutions for 2nth order lidstone BVP on time scales
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