Nodal solutions of nonlocal integral boundary value problems
Chamberlain, Jeremy E.
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In this dissertation, we study the nonlinear, non-local boundary value problem consisting of the second order equation -( p(t)y') ' + q(t) = w( t)f(y) on [a,b] and one of two boundary conditions involving a Riemann-Stieltjes integral. By relating the problems to the eigenvalues of the corresponding linear Sturm-Liouville problem with a two-point separated boundary condition, we obtain results on the existence and nonexistence of nodal solutions to these problems. The shooting method and a generalized energy function are used to prove the main results. We also discuss the changes in the existence of different types of nodal solutions as the problem changes. Finally, we examine a more general differential equation with multiple terms on the right hand side.