Existence and multiplicity of solutions for Kirchhoff–Schrödinger type equations involvingp(x)-Laplacian on the entire space

Jongrak Lee

¹

,

Jae‐Myoung Kim

²

,

Yun‐Ho Kim

³

A-priori bounds and multiplicity of solutions for nonlinear elliptic problems involving the fractionalp(⋅)-Laplacian

“…13) and hence,ˆBiˆBi |u n (x) − u n (y)| p − i |x − y| N +sp − i dx dy ≤ C 4 1 + k −q + * 2 nq + Z n ,(4 14). …”

A variable‐order fractional p(·)‐Kirchhoff type problem in ℝN

“…With the help of a direct variational approach and the theory of the variable exponent Sobolev spaces, the existence and multiplicity of solutions to a class of p ( x )‐ Kirchhoff‐type problems with Dirichlet boundary data were proved in Dai and Hao 4 . In Lee et al, 5 the existence and multiplicity of solutions for a class of p ( x )‐Kirchhoff type Schrödinger problems in was obtained by means of abstract critical point results. For more about the eigenvalue problem of this operator, we recommend the readers to refer to previous studies 6,7 …”

“…The proof of Theorems 1.1–1.2 are based on the application of an abstract critical point result for an energy functional fulfilling the Cerami condition, which can be found in Lee et al 5 For the reader's convenience, we now state the abstract critical point theorem.…”

An Optimal Control Problem Governed by a Kirchhoff-Type Variational Inequality

“…For more details on the physical and mathematical background of Kirchhoff-type problems, we refer the readers to the papers [1][2][3] and the references therein. By variational methods, many interesting results about the existence multiplicity of solutions for Kirchhoff-type problems have been established in the last ten years, see, e.g., [1][2][3][4][5][6][7] and the references therein.…”