# Multiplicity results for elliptic problems involving nonlocal integrodifferential operators without Ambrosetti-Rabinowitz condition

@article{Bonaldo2022MultiplicityRF, title={Multiplicity results for elliptic problems involving nonlocal integrodifferential operators without Ambrosetti-Rabinowitz condition}, author={L. M. M. Bonaldo and Olimpio Hiroshi Miyagaki and Elard Ju{\'a}rez Hurtado}, journal={Discrete \& Continuous Dynamical Systems}, year={2022} }

<p style='text-indent:20px;'>In this paper, we study the existence and multiplicity of weak solutions for a general class of elliptic equations <inline-formula><tex-math id="M1">\begin{document} $( \mathscr{P}_\lambda)$\end{document}</tex-math></inline-formula> in a smooth bounded domain, driven by a nonlocal integrodifferential operator <inline-formula><tex-math id="M2">\begin{document}$ \mathscr{L}_{\mathcal{A}K} $\end{document}</tex-math></inline-formula> with Dirichlet boundary conditions…

## 3 Citations

### On asymptotic behavior for a class of diffusion equations involving the fractional $$\wp (\cdot )$$-Laplacian as $$\wp (\cdot )$$ goes to $$\infty $$

- MathematicsRevista Matemática Complutense
- 2022

In this manuscript, we will study the asymptotic behavior for a class of nonlocal diffusion equations associated with the weighted fractional ℘(·)−Laplacian operator involving constant/variable…

### On a study and applications of the Concentration-compactness type principle for Systems with critical terms in $\mathbb{R}^{N}$

- Mathematics
- 2022

In this paper, we obtain some important variants of the Lions and Chabrowski Concentrationcompactness principle, in the context of fractional Sobolev spaces with variable exponents, especially for…

### Robin fractional problems with symmetric variable growth

- MathematicsJournal of Mathematical Physics
- 2020

In this paper we study the fractional p(., .)-Laplacian and we introduce the corresponding nonlocal conormal derivative for this operator. We prove basic properties of the corresponding function…

## References

SHOWING 1-10 OF 71 REFERENCES

### Existence and Multiplicity of Solutions for a Class of Elliptic Equations Without Ambrosetti–Rabinowitz Type Conditions

- Mathematics
- 2018

In this paper we establish, using variational methods, the existence and multiplicity of weak solutions for a general class of quasilinear problems involving $$p(\cdot )$$p(·)-Laplace type operators,…

### Existence of entire solutions for a class of quasilinear elliptic equations

- Mathematics
- 2013

The paper deals with the existence of entire solutions for a quasilinear equation $${(\mathcal E)_\lambda}$$ in $${\mathbb{R}^N}$$ , depending on a real parameter λ, which involves a general elliptic…

### Existence and Asymptotic Behaviour for a Kirchhoff Type Equation With Variable Critical Growth Exponent

- Mathematics
- 2017

AbstractIn this paper, we establish existence and asymptotic behaviour of nontrivial weak solution of a class of quasilinear stationary Kirchhoff type equations involving the variable exponent spaces…

### Multiplicity results for nonlinear Neumann boundary value problems involving p-Laplace type operators

- Mathematics
- 2016

We consider the existence of at least two or three distinct weak solutions for the nonlinear elliptic equations {−div(φ(x,∇u))+|u|p−2u=λf(x,u)in Ω,φ(x,∇u)∂u∂n=λg(x,u)on ∂Ω.$$ \textstyle\begin{cases}…

### Mountain pass type solutions and positivity of the infimum eigenvalue for quasilinear elliptic equations with variable exponents

- Mathematics
- 2015

AbstractWe study the following elliptic equations with variable exponents
$$-\text{div}(\phi(x,|\nabla u|)\nabla u)=\lambda f(x,u)\quad\text{in}\Omega$$-div(ϕ(x,|∇u|)∇u)=λf(x,u)inΩwhich is subject to…

### Trudinger-Moser type inequality and existence of solution for perturbed non-local elliptic operators with exponential nonlinearity

- Mathematics
- 2016

In this paper we consider the following perturbed nonlocal problem with exponential nonlinearity 1 \begin{document}$\begin{cases}-\mathcal{L}_{K}u+ \left|u\right|^{p-2}u+h(u)= f \ \ \ \ \ \mbox{in} \…

### Non-local Diffusion Equations Involving the Fractional $$p(\cdot )$$p(·)-Laplacian

- MathematicsJournal of Dynamics and Differential Equations
- 2019

In this paper we study a class of nonlinear quasi-linear diffusion equations involving the fractional $$p(\cdot )$$p(·)-Laplacian with variable exponents, which is a fractional version of the…

### ON SUPERLINEAR p(x)-LAPLACIAN-LIKE PROBLEM WITHOUT AMBROSETTI AND RABINOWITZ CONDITION

- Mathematics
- 2014

Abstract. This paper deals with the superlinear elliptic problem with-out Ambrosetti and Rabinowitz type growth condition of the form:−div(1 + |∇u| p(x) √ 1+|∇u| 2p(x) )|∇u| p(x)−2 ∇u= λf(x,u),…

### Ground state solutions of scalar field fractional Schrödinger equations

- Mathematics
- 2015

In this paper, we study the existence of multiple ground state solutions for a class of parametric fractional Schrödinger equations whose simplest prototype is $$\begin{aligned} (-\Delta…