Abstract
We investigate multiple solutions for the perturbation of a singular potential biharmonic problem with fixed energy. We get a theorem that shows the existence of at least one nontrivial weak solution under some conditions and fixed energy on which the corresponding functional of the equation satisfies the Palais-Smale condition. We obtain this result by variational method and critical point theory.
Highlights
Introduction and statement of main resultLet be a connected bounded domain of Rn with smooth boundary ∂, n ≥
We investigate the existence and multiplicity of weak solutions u ◦ x ∈ H for the perturbation of the biharmonic equation with singular potential
In [ ], by using degree theory we proved that when c < λ, λ (λ – c) < b < λ (λ – c), and s
Summary
Λk+m(λk+m – c) < < λk+m+ (λk+m+ – c), k ≥ , m ≥ , and conditions (A ) and (A ) hold. In Section , we introduce the eigenvalues and eigenfunctions of the eigenvalue problem u + c u – u = ku in , u = , u = on ∂ , introduce the eigenspaces spanned by the eigenfunctions of k = λk(λk – c) – , investigate the properties of eigenspaces and prove that the functional J(u ◦ x) satisfies the Palais-Smale condition. Proof First, we shall prove that J(u ◦ x) is continuous. |un (x(t))|p (t) dt un◦x H n is bounded, and there exists a constant C > such that [(|un(x(t))|q–. Q– q un◦x H is bounded, it follows from l < that the right-hand side of The embedding H → Lq( ) is compact, there exists a subsequence (uhn ◦ x)n such that lim [(|uhn
Sign-in/Register to view highlights & summary 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.
