Dirichlet problem with nonlinearity depending only on the derivative

✍ Scribed by N. Del Toro; P. Girg; F. Roca

• Book ID: 104349423
• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 287 KB
• Volume: 16
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/s0893-9659(02)00137-4

✦ Synopsis

We study the existence of solutions for the following problem:

u"(t) + u(t) + g (u'(t)) = f(t), t E (0, 7r), u(O) = u(~) = O,

(1)

where f E C[0, ~], g E C(R) is bounded and has limits limu~±oo g(u). We also give information on the set of f for those that solution exists, relating it with the corresponding linear problem. (~) 2002 Elsevier Science Ltd. All rights reserved.