Global structure of nodal solutions for second-order -point boundary value problems with superlinear nonlinearities.
We consider boundary value problems for nonlinear th-order eigenvalue problem where and for some , and for , and , where . We investigate the global structure of positive solutions by using Rabinowitz’s global bifurcation theorem.
Sufficient conditions for the existence of solutions to boundary value problems with a Caratheodory right hand side for ordinary differential systems are established by means of continuous approximations.
The nonlocal boundary value problems for linear and nonlinear degenerate abstract differential equations of arbitrary order are studied. The equations have the variable coefficients and small parameters in principal part. The separability properties for linear problem, sharp coercive estimates for resolvent, discreetness of spectrum and completeness of root elements of the corresponding differential operator are obtained. Moreover, optimal regularity properties for nonlinear problem is established....