The maximum principle and some applications for the fourth order nonlinear elliptic differential equations

SUMMARY Master Thesis THE MAXIMUM PRINCIPLE AND SOME APPLICATIONS FOR THE FOURTH ORDER NONLINEAR ELLIPTIC DEFERENTIAL EQUATIONS Hikmet YAMAN Fırat University Graduate School of Natural and Applied Sciences Department of Mathematics 2005, Page : 53 This thesis consists of five chapters. In the first chapter, some fundamental definitions and theorems are given. In the second chapter, it is established the maximum principle for the second order elliptic operators, stated generalizations and given some applications. In the third chapter, it is investigated nonlinear operators and the maximum principle for the second order nonlinear elliptic operators and some applications are given. In the fourth chapter, it is investigated the maximum principle for the fourth order elliptic partial differential equations. In the last chapter, some applications related to the maximum principle for the elliptic equations are given. KEY WORDS: Maximum principle, Elliptic, Laplace operator, Biharmonic operator, Nonlinear elliptic equations. rv