CEU Electronic Theses and Dissertations, 2010
| Author | Gyulov, Tihomir Bogomilov |
|---|---|
| Title | Solvability of Some Nonlinear Fourth Order Boundary Value Problems |
| Summary | This thesis is concerned with the study of certain classes of nonlinear fourth order boundary value problems. They are motivated by some physical problems. Sufficient conditions for the existence of solutions under various assumptions are presented. After an introductory chapter, we discuss (in Chapter 2) a fourth order equation involving a quite general nonlinearity. A variant of the method of lower and upper solutions is presented. The existence of a solution located between suitable lower and upper solutions is proved. Practical examples show that the hypotheses of the main results hold for a wide range of differential equations. A direct application to the extended Fisher-Kolmogorov equation provides some sharp estimates for its stationary periodic solutions. Next, in Chapter 3, a class of fourth order differential inclusions involving the p-biharmonic operator is investigated. It is related to the beam-column theory. The existence of solutions for a wide class of boundary conditions is proved. The problem is treated variationally, via the critical point theory for non-smooth functionals. Some of the results concern mountain pass type solutions. |
| Supervisor | Morosanu, Gheorghe |
| Department | Mathematics PhD |
| Full text | https://www.etd.ceu.edu/2010/tphgyt01.pdf |
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