[PDF] Top 20 On the Existence of Solutions of a Nonlocal Elliptic Equation with a p Kirchhoff Type Term

... the nonlocal term Mu p 1,p motivated, among other things, by the above physical ...the p-Laplacian operator that appears in several areas of the science such as astronomy, glaciology, ... See full document

... this type of equation in recent years, and we refer to [9, 13, 27] and the references ...the existence of solutions of p- biharmonic equations has been studied by several authors; see ... See full document

... | u t |   u t . K. Ono and K. Nishihara [4] have proved the global existence and decay structure of solutions of (1.1)-(1.3) without small condition of data using Galerkin method. K. Ono [5] has obtained ... See full document

... In this paper, we prove the global existence for the problem (.)-(.) by applying the po- tential well theory introduced by Sattinger [] and Payne and Sattinger []. Meanwhile, we obtain the asymptotic ... See full document

... some phenomena appearing in different physical, engineering and other sciences because it is regarded as a good approximation for describing nonlinear vibrations of beams or plates (see [, ]). By using the fixed point ... See full document

... (6) We also refer the reader to the papers [22, 39, 48] for such other fourth-order problems. On the other hand, singular elliptic problems have been intensively studied in recent years, see for example, [25, 26, ... See full document

... Vries type equation with the external ...KDV type equations in [1]- [4]. In that paper the equation is reduced to the system of integral ... See full document

... the solutions of a nonlocal elliptic system of (p,q)-Kirchhoff type on a bounded domain based on the three critical points theorem introduced by ...the existence of three weak ... See full document

... [15] J.-L. Lions, On some questions in boundary value problems of mathematical physics, Contempo- rary Developments in Continuum Mechanics and Partial Differential Equations (Rio de Janeiro, 1977), North-Holland Math. ... See full document

... where c ∈ R, c / 0 and g, h : R → R. First we consider 1.2 as a perturbation of the nonlocal system and prove that if g and h grow linearly, then 1.2 has a solution provided |c| is not too large. Afterwards, ... See full document

... a nonlocal parabolic equation with time-integral term does not seem to be so much investigated as nonlocal equations with space-integral ...memory term has some difficulties in proving ... See full document

... self. Nonlocal effect also finds its applications in biological ...integral term, is assumed to be dependent on the energy of the entire system with u being its population ... See full document

... previous existence results and, in particular, those of the aforementioned papers, no growth condition is required on f. Indeed, we only require that on a certain interval 0, C the function fx, · is bounded from ... See full document

... of solutions admitted subject to the vari- ations of parameters embedded in nonlinear ...the existence and multiplicity of positive solutions for the elliptic equations has been extensively ... See full document

... In this article we will use the following sub-supersolution principle, the proof of which is based on the well known fixed point theorem for the increasing operator on the order interval (see e.g., [45]) and is similar ... See full document

... the existence and multiplicity of positive solutions for an interesting nonlocal differential equation using the Cone-Compression and Cone-Expansion Theorem due to ...the existence ... See full document

... flux term J. The flux term J is a vector field that explains a movement of some physical contents u such as temperature, chemical potential, electrostatic potential, or fluid ...|∇u| p−2 ∇u is to ... See full document

... the existence and multiplicity of solutions to problem ...an elliptic equation coupled with a non-local ...non-local term with the critical nonlinearity and the lack of compactness of ... See full document

... began to attract the attention of several researchers only after Lion [] had proposed an abstract framework for this problem. Perera and Zhang [] obtained a nontrivial solution of () by using the Yang index and ... See full document

... There has been an increasing interest in studying equations involving p ( x )-Laplace operators over the last few decades. Motivated by theoretical re- search in the regularizing effect of the interaction between ... See full document