Existence of solutions for fourth order elliptic equations of Kirchhoff type

Sign-changing solutions for fourth order elliptic equations with Kirchhoff-type

“…Later, in [19], Recently, in [20,21], Ma and obtained the existence and multiplicity of solutions. In [29], by inserting a parameter λ, the authors considered the existence of nontrivial solutions for (1.2) with λ. Recently, Xu and Chen [31,32,33] obtained infinitely many large energy solutions and negative energy solutions to (1.1), respectively.…”

On Fourth-Order Elliptic Equations of Kirchhoff Type with Dependence on the Gradient and the Laplacian

“…The existence of a nontrivial solution of (1) is established when we choose appropriate * such that 0 < < * . The paper generalized the conclusions in [7,14] and weakened the condition in [7]. In the following research work, we will also consider problem (1), but we just truncate the right side of the equation, and the left of the equation remains the same.…”

“…We refer the readers to [10][11][12][13][14][15][16][17][18][19][20]. Particularly, Wang et al studied the following fourthorder equation of Kirchhoff type equation…”

On the existence of solutions for a class of fourth order elliptic equations of Kirchhoff type with variable exponent

“…We point out that if p(.) is a constant then problem (1) has been studied by many authors in recent years, we refer to some interesting papers [3,8,15,19,23,27,28,29]. In [29], Wang and An considered the following fourth-order elliptic equation…”