[PDF] Top 20 Existence and concentration of solutions for the nonlinear Kirchhoff type equations with steep well potential

... and Corollary ., we can obtain the conclusion of Theorem .. Proof of Theorem . For the case V ≥ , we can easily prove that the functional I satis- fies the conditions of mountain-pass theorem, and therefore, the ... See full document

... a steep potential well. They obtained the existence and multiplicity of nontrivial solution for problem (3) with λ large ...nontrivial solutions with λ large enough and β < ... See full document

... energy solutions of problem ...the existence and the non-existence of nontrivial solution of problem ...the concentration of solution. Liu and He [] discussed the existence of ... See full document

... this type of nonlinearity furnishes a model to study traveling waves in suspension ...the existence of at least one solution, or multiple solutions, or even infinitely many solu- tions for ... See full document

... with steep well potential and establish the existence of nontrivial solution and concentration results (as λ → ∞) under some mild assumptions (where, f (x, u) is sublinear and ... 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 ... See full document

... the existence and blow up of the solution for the problem ...global existence and decay of the solution for the ...global existence, blow up and decay of the solution for the problem ...global ... See full document

... the existence of solutions for fractional Kirchhoff equation like ...state solutions for ...the existence of ground state solutions by using the monotonicity trick and the profile ...the ... See full document

... the existence of weak solutions for problem (P) without assuming the (AR) condition, but imposing various assumptions for the diver- gence part ϕ and nonlinear term f ...the nonlinear term f ... See full document

... the type (6) and a > 0, b ≥ 0 , problem (1) is said to be non-degenerate, while it is called degenerate if a = 0 ...usual well-known quasilinear elliptic equation while a > 0, b = 0 ...The ... See full document

... 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] ... See full document

... The content of this paper is organized as follows. In Section 2, we give some lemmas. In Section 3, we prove the existence and uniqueness of the local solution by the Banach contraction mapping principle. In ... See full document

... longer a pointwise identical equation. This phenomenon provokes more difficulties to overcome, which makes the study of such a class of problems particularly interesting. If the function V vanishes and R N is replaced with ... See full document

... In recent years, various Kirchhoff-type problems have been widely discussed by lots of authors. The Kirchhoff mode is an extension of the classical D’Alembert’s wave equation for free vibrations of elastic strings, ... See full document

... the Kirchhoff equations and the Kirchhoff systems have been considered by variational method in the case involving the p − Laplacian operator [4, 7, 8, 18, 19, ...differential equations with ... See full document

... a nonlinear Fredholm equa- tion expressed as a perturbed linear ...the existence of a solution of some special cases of ...general nonlinear integral equation has the following ... See full document

... the existence and multiplicity of weak solutions for problem (1) by using variational methods, for example, the nonlinear- ity f is asymptotically 3-linear at infinity (see [4, 6, 9]), the ... See full document

... the existence of nonoscillatory solutions of second order nonlinear neutral differential ...some well-known results for linear and nonlinear equa- ...the existence of ... See full document

... u x = u x u x = u x x ∈ Ω ⊂ (13) They mainly use the Ornstein-Uhlenbech process to deal with the stochastic term of Equation (11), thus obtain the global well-posedness of the solution, and then prove the ... See full document

... In this section, we consider the existence of random attractor family. To deal with the random term we need to transform the problem (1.1) - (1.3) into a gen- eral stochastic problem. It is proved that there ... See full document