The Nehari Manifold Of Nonlinear Elliptic Equations

In this paper, we investigate the Nehari manifold of nonlinearelliptic equations. In chapter one, we study the Nehari manifold of a nonlinearproblems involving concave and convex terms. Basing on the extraction ofPalais-Smale sequences in the Nehari manifold, we discuss the existence of thepositive solutions of the equations. In chapter two, we discuss the nonlinearelliptic problems with unbounded coe?cients on the unbounded domain RN.Combining the compact embedding Proposition in H, we use two methods toobtain the existence of the nonradial solutions of this equations. In chapterthree, we discuss the Nehari manifold of the nonlinear elliptic equations inWeight Sobolev space. By investigating the compact imbedding theorem andthe properties of homogeneous eigenvalue problem in weighted Sobolev spaceand exploiting the relationship between the Nehari manifold and fibreringmaps, we discuss the properties of the Nehari manifold. Using these propertieswe also derive out the existence and non-existence results for positive solutionsof the equations.