𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Existence of Solutions to u″ + u + g(t, u, u′) = p(t), u(0) = u(π) = 0

✍ Scribed by R. Kannan; S. Seikkala

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
98 KB
Volume
263
Category
Article
ISSN
0022-247X

No coin nor oath required. For personal study only.

✦ Synopsis

are presented. The proofs are based on the alternative method, a connectedness result, the contraction mapping principle, and a detailed analysis of the bifurcation equation utilizing, e.g., a generalization of the mean value theorem for integrals. We shall obtain results with g bounded or unbounded, having finite limits at ±∞ or without limits, thus extending some recent results in the literature. The proofs offer a constructive way to find the bounds for p and to find numerically the number of solutions and the approximative solutions.

📜 SIMILAR VOLUMES

Calculating the Galois Group of Y′ 
Calculating the Galois Group of Y′ =   =   =  AY +   +   +  B,Y′ =   =   =  AY Completely Reducible
✍ Peter Berman 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 291 KB

We consider a special case of the problem of computing the Galois group of a system of linear ordinary differential equations Y = M Y , M ∈ C(x) n×n . We assume that C is a computable, characteristic-zero, algebraically closed constant field with a factorization algorithm. There exists a decision pr

Precise Spectral Asymptotics for the Dir
Precise Spectral Asymptotics for the Dirichlet Problem − u″(t) + g(u(t)) = λsinu(t)
✍ Tetsutaro Shibata 📂 Article 📅 2002 🏛 Elsevier Science 🌐 English ⚖ 163 KB

where λ > 0 is a parameter and T > 0 is a constant. It is known that if λ 1, then the corresponding solution has boundary layers. In this paper, we characterize λ by the boundary layers of the solution when λ 1 from a variational point of view. To this end, we parameterize a solution pair λ u by a n