showing 2 related works from this author
Dirichlet Boundary Value Problem for the Second Order Asymptotically Linear System
2016
We consider the second order system x′′=f(x) with the Dirichlet boundary conditions x(0)=0=x(1), where the vector field f∈C1(Rn,Rn) is asymptotically linear and f(0)=0. We provide the existence and multiplicity results using the vector field rotation theory.
Types of solutions and multiplicity results for two-point nonlinear boundary value problems
2005
Abstract Two-point boundary value problems for the second-order ordinary nonlinear differential equations are considered. If the respective nonlinear equation can be reduced to a quasi-linear one with a non-resonant linear part and both equations are equivalent in some domain D , and if solutions of the quasi-linear problem lie in D , then the original problem has a solution. We then say that the original problem allows for quasilinearization. We show that a quasi-linear problem has a solution of definite type which corresponds to the type of the linear part. If quasilinearization is possible for essentially different linear parts, then the original problem has multiple solutions.