Multiplicity of solutions for critical Kirchhoff type equations

We prove the existence of multiple solutions for critical Kirchhoff equations involving positive operators in closed manifolds.     

Nontrivial solutions of Kirchhoff type problems

In this work, we study Kirchhoff type problems on a bounded domain. We consider the cases where the nonlinearity is superlinear near zero but asymptotically 4-linear at infinity, and the nonlinearity is asymptotically linear near zero but 4-superlinear at infinity. By computing the relevant critical groups, we obtain nontrivial solutions via Morse theory.     

Existence and multiplicity of solutions for Kirchhoff type equations

In this paper, the existence and multiplicity of weak solutions are obtained for a class of Kirchhoff type problems with Dirichlet boundary value conditions by using the mountain pass theorem, the local linking theorem, the fountain theorem and the symmetric mountain pass lemma in critical point theory.     

Positive solutions for p‐Kirchhoff type problems on

In this paper, we establish the existence and non‐existence of positive solutions for p‐Kirchhoff type problems with a parameter on without assuming the usual compactness conditions. We show that the p‐Kirchhoff type problems have at least one positive solution when the parameter is small, while the p‐Kirchhoff type problems have no positive solutions when the parameter is large. Our argument is based on variational methods, monotonicity methods, cut‐off functional techniques, and a priori estimates techniques. Copyright © 2014 John Wiley & Sons, Ltd.     

Multiplicity of positive solutions for a class of quasilinear nonhomogeneous Neumann problems

In this paper we study the existence, nonexistence and multiplicity of positive solutions for nonhomogeneous Neumann boundary value problem of the type

where Ω is a bounded domain in with smooth boundary, 1<p<n,Δ_pu=div(|u|^p-2u) is the p-Laplacian operator, , , (x)0 and λ is a real parameter. The proofs of our main results rely on different methods: lower and upper solutions and variational approach.     

Nonexistence and existence of positive solutions for the Kirchhoff type equation

In this paper, we study the nonexistence and existence of positive solutions for the Kirchhoff type equation with nonlinearity having prescribed asymptotic behavior. Because of the structure of our equation, our nonexistence results have some special properties, and our conditions for positive solutions are also different from the existing results.     

带有类p-Laplacian算子的Kirchhoff型方程的多重解

研究一类带有类p-Laplacian算子的Kirchhoff型方程.利用对称山路定理,得到了多重解存在的充分条件,推广和改进了已有结果.     

Low regularity global solutions for nonlinear evolution equations of Kirchhoff type

We study the global solvability of the Cauchy-Dirichlet problem for two second order in time nonlinear integro-differential equations:

1)

the extensible beam/plate equation

     

Multiplicity of positive solutions for a class of elliptic equations in divergence form

We prove results concerning the existence and multiplicity of positive solutions for the quasilinear equation

     

Multiplicity of positive solutions for semilinear elliptic problems in unbounded domains

In this paper, we study the effect of domain shape on the multiplicity of positive solutions for the semilinear elliptic equations. We prove a Palais-Smale condition in unbounded domains and assert that the semilinear elliptic equation in unbounded domains has multiple positive solutions.     

Existence and multiplicity of the solutions of the p(x)–Kirchhoff type equation via genus theory

In this paper, by using variational approach and Krasnoselskii's genus theory, we show the existence and multiplicity of the solutions of the p(x)‐Kirchhoff type equation. Copyright © 2011 John Wiley & Sons, Ltd.     

Existence and multiplicity of positive solutions for a class of singular Kirchhoff type problems with sign‐changing potential

In this paper, the existence and multiplicity of positive solutions are obtained for a class of Kirchhoff type problems with two singular terms and sign‐changing potential by the Nehari method.     

One-bump positive solutions for the Kirchhoff equations with perturbation in

In this paper, we study the Kirchhoff equations with perturbation in . Applying the finite reduction method, we prove that the equation has one-bump positive solutions under some suitable conditions that are given in Section 1.     

Existence of positive solutions to Kirchhoff type problems with zero mass

The existence of positive solutions depending on a nonnegative parameter λ to Kirchhoff type problems with zero mass is proved by using variational method, and the new result does not require usual compactness conditions. A priori estimate and a Pohozaev type identity are used to obtain the bounded Palais–Smale sequences for constant coefficient nonlinearity, while a cut-off functional and Pohozaev type identity are utilized to obtain the bounded Palais–Smale sequences for the variable-coefficient case.     

Kirchhoff type problems involving $p$-biharmonic operators and critical exponents

In this paper, we study the existence of solutions for a class of Kirchhoff type problems involving $p$-biharmonic operators and critical exponents. The proof is essentially based on the mountain pass theorem due to Ambrosetti and Rabinowitz [2] and the Concentration Compactness Principle due to Lions [18,19].     

Multiple positive solutions for Kirchhoff type problems with singularity and asymptotically linear nonlinearities

In this paper, we devote ourselves to investigating a nonlocal problem involving singularity and asymptotically linear nonlinearities. By using the variational and perturbation methods, we obtain the existence of two positive solutions which improve the existing result in the literature.     

Multiple positive solutions for Kirchhoff type of problems with singularity and critical exponents

In this paper, we study multiplicity of positive solutions for a class of Kirchhoff type of equations with the nonlinearity containing both singularity and critical exponents. We obtain two positive solutions via the variational and perturbation methods.