Kirchhoff-Type Equations
Hausdorff Dimension and Fractal Dimension of the Global Attractor for the Higher Order Coupled Kirchhoff Type Equations
... Guoguang Lin and Sanmei Yang [1] had studied the existence and uniqueness of the solution and global attractors for the higher-order coupled Kirchhoff-type equations. Furthermore, we consider the ...
14
The Inertial Manifolds for a Class of Higher Order Coupled Kirchhoff Type Equations
... DOI: 10.4236/jamp.2018.65091 1064 Journal of Applied Mathematics and Physics er-order coupled Kirchhoff-type equations. In the process of research, we take advantage of Hadamard’s graph to get the ...
10
Existence of Positive Solutions for a Coupled System of Kirchhoff Type Equations with Sobolev Critical Exponent
... with Kirchhoff type, Acta Mathematicae Applicatae Sinica, 32 (2016) ...of Kirchhoff type equations, Electronic Journal of Qualitative Theory of Differential Equations, 6 (2014) ...
13
The Inertial Manifold for Class Kirchhoff Type Equations with Strongly Damped Terms and Source Terms
... In this paper, we study the inertial manifolds for a class of the Kirchhoff-type equations with strongly damped terms and source terms. The inertial mani- fold is a finite dimensional invariant ...
8
Estimate on the Dimension of Global Attractor for Nonlinear Higher Order Coupled Kirchhoff Type Equations
... G. G. Lin and L. J., Hu have studied the existence of a global attractor for coupled Kirchhoff type equations with strongly linear damping in [1]. In this paper, we are concerned with the finite ...
14
Existence and multiplicity of positive solutions for a class of p ( x )-Kirchhoff type equations
... of Kirchhoff type equations has already been extended to the case involving the p-Laplacian (for details, see [27-29]) and p(x)-Laplacian (see ...
16
The Estimates of the Upper Bounds of Hausdorff Dimensions for the Global Attractor for a Class of Nonlinear Coupled Kirchhoff Type Equations
... How to cite this paper: Lin, G.G. and Zhang, M. (2018) The Estimates of the Upper Bounds of Hausdorff Dimensions for the Global Attractor for a Class of Non- linear Coupled Kirchhoff-Type Equations. ...
10
The Exponential Attractor for a Class of Kirchhoff Type Equations with Strongly Damped Terms and Source Terms
... Although the study of exponential attractors has continued to develop, the study of the exponential attractors of the system of equations is not universal. As a result, this has spurred our desire to explore the ...
13
On existence and multiplicity of solutions for Kirchhoff-type equations with a nonsmooth potential
... To the best of our knowledge, there exist few results on studying the Kirchhoff-type problems with nonsmooth potentials. We will face at least two difficulties in treating prob- lem (.). Firstly, the presence of ...
18
On the sub supersolution method for p(x) Kirchhoff type equations
... local minimizer of the integral functional J in the C topology. In [], Fan established a Brezis-Nirenberg type theorem (Theorem . of []), which asserts that every local min- imizer of J in the C () ...
11
Existence and concentration of solutions for the nonlinear Kirchhoff type equations with steep well potential
... In this paper, by using the variational methods, the existence of nontrivial solutions and the concentration phenomena of the solutions to equation (.) were established.. We consider ([r] ...
15
Multiplicity and asymptotic behavior of solutions to a class of Kirchhoff type equations involving the fractional p Laplacian
... existence of infinitely many solutions which tend to zero for suitable positive parameters ξ and τ by the Kajikiya version of the symmetric mountain-pass theorem. Some other important and meaningful results on the ...
19
Multiplicity of nontrivial solutions for a class of nonlinear Kirchhoff-type equations
... they verified that the problem has a positive ground state solution that the result can be viewed as a partial extension of [] where the authors studied the existence and con- centration behavior of positive solutions of ...
12
Blow up of Solutions for a System of Nonlinear Higher order Kirchhoff type Equations
... Ono [16] considered equation (1.3) with M (s) = s γ , m = 1 and showed that the solution blow up if the initial energy is negative. Wu and Tsai [23] showed that the solution blow up under the condition of positive upper ...
11
RETRACTED ARTICLE: Sign changing solutions to Schrödinger Kirchhoff type equations with critical exponent
... modulus). Equations of this type arise in the study of string or membrane vibration and were proposed by Kirchhoff in (see []) to describe the transversal os- cillations of a stretched string, ...
14
Multiple positive solutions for a class of Kirchhoff type equations in \(\mathbb{R}^{N}\)
... Li, G, Ye, H: Existence of positive ground state solutions for the nonlinear Kirchhoff type equations in R 3. Liu, Z, Guo, S: Existence of positive ground state solutions for Kirchhoff typ[r] ...
13
Existence of nontrivial weak solutions for p-biharmonic Kirchhoff-type equations
... differential equations arise in the study of deflections of elastic beams on nonlinear elastic ...this type of equation in recent years, and we refer to [9, 13, 27] and the references ...biharmonic ...
17
Multiplicity and asymptotic behavior of solutions for Kirchhoff type equations involving the Hardy–Sobolev exponent and singular nonlinearity
... By the variational method, they obtained the existence and multiplicity of positive solu- tions to the above problem. Subsequently, an increasing number of researchers have paid attention to semilinear elliptic ...
19
Existence of nontrivial solutions for p-Kirchhoff type equations
... In this paper, the linking theorem and the mountain pass theorem are used to show the existence of nontrivial solutions for the p -Kirchhoff equations without assuming Ambrosetti-Rabinowi[r] ...
9
On the Exponential Decay of Solutions for Some Kirchhoff Type Modelling Equations with Strong Dissipation
... nonlinear Kirchhoff-type equations with strong dissipative and source terms u tt ( u 2 2 ) u a u t b u | | 2 u x , , t 0 in a bounded domain, where a b , 0 and 2 are ...
5