Abstract
Existence of sign-changing solutions to quasilinear elliptic equations of the form [Formula: see text] under the Dirichlet boundary condition, where [Formula: see text] ([Formula: see text]) is a bounded domain with smooth boundary and [Formula: see text] is a parameter, is studied. In particular, we examine how the number of sign-changing solutions depends on the parameter [Formula: see text]. In the case considered here, there exists no nontrivial solution for [Formula: see text] sufficiently small. We prove that, as [Formula: see text] becomes large, there exist both arbitrarily many sign-changing solutions with negative energy and arbitrarily many sign-changing solutions with positive energy. The results are proved via a variational perturbation method. We construct new invariant sets of descending flow so that sign-changing solutions to the perturbed equations outside of these sets are obtained, and then we take limits to obtain sign-changing solutions to the original equation.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
