ISSN:
0170-4214
Keywords:
Mathematics and Statistics
;
Applied Mathematics
Source:
Wiley InterScience Backfile Collection 1832-2000
Topics:
Mathematics
Notes:
We consider the existence of a nontrivial solution of the following equation: \documentclass{article}\pagestyle{empty}\begin{document}$$ \begin{array}{l} \begin{array}{*{20}c} {} & {u_{tt} + u_{xxxx} + g(u) = 0} & {(x,t) \in Q = (0,\pi ) \times (0,2\pi )} \\ \end{array} \\ \begin{array}{*{20}c} {(0)} & {u(0,t) = u(\pi,t) = u_{xx} (\pi,t) = 0,t \in (0,2\pi )} & {} \\ \end{array} \\ \begin{array}{*{20}c} {} & {u(x,0) = (x,2\pi ),} & x \\ \end{array} \in (0,\pi ) \\ \end{array} $$\end{document} where g is a nondecreasing function defined on R1, satisfies g(O) = O, and some other additional conditions.Our results and methods are quite similar to those associated with recent work on the nonlinear wave equation [1]-[8]: \documentclass{article}\pagestyle{empty}\begin{document}$$ \begin{array}{l} \begin{array}{*{20}c} {u_{tt} - u_{xx} + g(u) = 0} & {(x,t) \in 0} \\ \end{array} \\ \begin{array}{*{20}c} {u(0,t) = u(\pi,t) = 0} & {t\varepsilon (0,2\pi )} \\ \end{array} \\ \begin{array}{*{20}c} {u(x,0) = u(x,2\pi )} & {x\varepsilon (0,\pi )} \\ \end{array} \\ \end{array} $$\end{document} .
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1002/mma.1670040113
Permalink
