Existence of positive solutions for the nonlinear Kirchhoff type equations in Rn

Existence of Infinitely Many High Energy Solutions for a Fourth-Order Kirchhoff Type Elliptic Equation in R<sup>3</sup>

“…To get over the difficulty, we suppose that the potential V (x) satisfies the conditions (V0) and (V1). The result obtained in this paper can be seemed as a generalization of the related result obtained in [20] when N = 3.…”

“…In [19], Almuaalemi, Chen and Khoutir combined the variational methods and Symmetric Mountain Pass Theorem to research the existence of high energy solutions for problem (1.1) with a nonlinearity f (x, u). In [20], Xu obtained positive solutions for a class of second-order nonlinear Kirchhoff type equations in R N . Motivated primarily by the above-mentioned results, we will investigate infinitely many high energy solutions for problem (1.1) and obtain some results by variational methods.…”

Existence of Positive Solutions for the Kirchhoff Type Equations Involving General Critical Growth in \(\mathbb{R}\)\(^{N}\)

“…Problem (1.4) is the special form of the problem (1.1), in other words, problem (1.1) is more general than problem (1.4). Hence, our results can be seemed as the complementary work of [25].…”

“…Although the Kirchhoff-type Dirichlet problem have been extensively studied, as far as we know, there is very little literature on Kirchhoff-type problems (such as (1.1)), which involved parameters. Very recently, Xu [25] studied the following nonlinear Kirchhoff type equations…”

Mathematical behavior of solutions of the Kirchhoff type equation with logarithmic nonlinearity

“…So that, Kirchhoff model was very important for many applications in mechanics, elastic theory and other areas of mathematical physics [3]. It is worth noting that there have been mang interesting study of the with initial and boundary value problems for Kirchhoff type equation, for details on Kirchhoff type equation, we refer to see the works [9,13,19,20,23] The original equation is…”