Construction Of Lower And Upper Solutions For Some Nonlinear Differential Equations And Its Applications

This dissertation mainly constructs the lower and upper solutions for first-order periodic problem, second-order Neumann problem and the mean curvature equation in an annular domain. By using the method of lower and upper solutions, we obtain several existence results of solutions for the corresponding nonlinear problems. The main works of the paper are as follows.1. we construct nonconstant upper and lower solutions for the first-order periodic boundary value problem where f:[0,T] × Râ†' R is continuous. Moreover, we give the bounds estimates for lower and upper solutions and obtain the existence results of solutions. In addition, we prove the existence of positive solutions for the singular problem where g:(0, ∞) â†' R is continuous and g may be singular at x= 0.2. we establish the method of lower and upper solutions and obtain the existence results of solutions for the second-order Neumann boundary value problem wherc f:[0, T] × Râ†'R is L1-Caratheodory.3. by constructing lower and upper solutions, we obtain existence of radial solutions of the following mean curvature equation with Neumann boundary condition in annular where A, B ∈ R, 0 < A < B, D = {x ∈ RN : A ≤ |x| ≤ B}. f : [A, B] × R2 â†' R is continuous function, dr/dv represents the radial derivative and (αv/αv) is outward normal derivative of v. The main results give a complement for the corresponding results of Bereanu, Jebelean and Mawhin’s [ Math. Nachr., 2010].