A new approach in studying one parameter nonlinear eigenvalue problems with constraints

The paper presents a new approach for obtaining existence and location of solutions to nonlinear eigenvalue problems depending on a parameter and subject to constraints. The location of eigensolutions and subsequent parameters is achieved by means of the graph of the derivative of a function used also to compensate the lack of coercivity. The applications concern one parameter families of semilinear elliptic eigenvalue problems with Dirichlet boundary conditions for which various qualitative properties of the solution sets are established.