Abstract
In this paper, we study the following fourth-order elliptic equations of Kirchhoff type: , in , , where are constants, we have the potential and the nonlinearity . Under certain assumptions on and , we show the existence and multiplicity of negative energy solutions for the above system based on the genus properties in critical point theory. MSC: 35J20, 35J65, 35J60.
Highlights
Introduction and main resultsConsider the following fourth-order elliptic equations of Kirchhoff type: ⎧⎨ u – (a + b R |∇u| dx) u + V (x)u = f (x, u) in R, ⎩u ∈ H (R ), ( . )where a, b are positive constants
We study the following fourth-order elliptic equations of Kirchhoff type: 2u – (a + b R3 |∇u|2 dx) u + V(x)u = f (x, u), in R3, u ∈ H2(R3), where a, b > 0 are constants, we have the potential V(x) : R3 → R and the nonlinearity f (x, u) : R3 × R → R
Motivated by the above works described, the object of this paper is to study the existence and multiplicity solutions for a class of sublinear fourth-order elliptic equation of Kirchhoff type by using the genus properties in critical theory
Summary
([ ]) Let I be an even C functional on E and satisfy the (PS)-condition. Assume that (V) and (f )-(f ) hold, I is bounded from below and satisfies the (PS)-condition. Assume that {un} ⊂ E is a sequence such that {I(un)} is bounded and I (un) → as n → ∞ C = infE I(u) is a critical value of I, that is, there exists a critical point u∗ such that I(u∗) = c. I ∈ C (E, R) is bounded from below and satisfies the (PS)-condition. It follows from (f ) that I is even and I( ) =.
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 call
