A nonlocal boundary value problem with singularities in phase variables

✍ Scribed by S. Staněk

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 892 KB
• Volume: 40
• Category: Article
• ISSN: 0895-7177
• DOI: 10.1016/j.mcm.2003.11.003

✦ Synopsis

The singular differential equation (g(x')) ' = f(t, x, x') together with the nonlocal boundary conditions x(0) = x(T) = -Tmin{x(t) : t E [0,T]} is considered. Here g E C°(]R) is an increasing and odd function, positive f satisfying the local Carath4odory conditions on [0, T] × (]R \ {0}) 2 may be singular at.the value 0 in all its phase variables and 7 E (0, co). The existence result for the above boundary value problem is proved by the regularization and sequential techniques. Proofs use the topological transversality principle and the Vitali's convergent theorem.