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Existence and Nonexistence of Solutions of Nonlinear Dirichlet Problems with First Order Terms

✍ Scribed by Luisa Moschini; Stanislav I. Pohozaev; Alberto Tesei

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
141 KB
Volume
177
Category
Article
ISSN
0022-1236

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✦ Synopsis

Existence theorems for nonnegative solutions to a class of nonlinear Dirichlet problems with first order terms are proved. Nonexistence results are also discussed, depending on the regularity of the coefficient of the first order term. The proofs make use of a direct variational approach and of integral identities.

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✍ Changming Song; Zhijian Yang πŸ“‚ Article πŸ“… 2009 πŸ› John Wiley and Sons 🌐 English βš– 207 KB πŸ‘ 1 views

The paper studies the existence and nonexistence of global solutions to the Cauchy problem for a nonlinear beam equation arising in the model in variational form for the neo-Hookean elastomer rod where k 1 ,k 2 > 0 are real numbers, g(s) is a given nonlinear function. When g(s) = s n (where n 2 is