Existence Of The Solutions To Semilinear Elliptic Equations

This thesis research object is semilinear elliptic equations of the existence of the solutions for the problems. This paper applied the fixed point theory and upper and lower solution method to research the existence of the solutions for the equationsIn the first part of the paper, we research such as semilinear elliptic equations, and join the following constraints, u,u ?C2 (?) ?C(?), s.t.The existence of the solutions for the equations and the relationship between ?1 and ?2. Usually, we use the variational method research to this problem. First prove the equation meet the PS condition, the prove the existence of the solution. In this paper, we study the problem by using fixed point theorems and copying of upper and lower solution.In the second part of the paper, we research such as semilinear elliptic equations. Here, also no application of variational method, and only use the method of upper and lower solutions iterative structure convergence of upper and lower solutions sequence, then we proof that the convergence points to the sequence is the solution of the equation. Finally, we will also results generalize to more general case. And such as semilinear elliptic equations.