Related papers: Existence and multiplicity results for Kirchhoff t…
In this work, we establish some abstract results on the perspective of the fractional Musielak-Sobolev spaces, such as: uniform convexity, Radon-Riesz property with respect to the modular function, $(S_{+})$-property, Brezis-Lieb type Lemma…
We establish a concentration-compactness principle for the Sobolev space $W^{2,p(\cdot)}(\Omega)\cap W_0^{1,p(\cdot)}(\Omega)$ that is a tool for overcoming the lack of compactness of the critical Sobolev imbedding. Using this result we…
Firstly, we use Nehari manifold and Mountain Pass Lemma to prove an existence result of positive solutions for a class of nonlocal elliptic system with Kirchhoff type. Then a multiplicity result is established by cohomological index of…
Using variational methods, we obtain several multiplicity results for double phase problems that involve variable exponents and a new type of critical growth. This new critical growth is better suited for double phase problems when compared…
In this paper, we prove the existence and multiplicity of solutions for a large class of quasilinear problems on a nonreflexive Orlicz-Sobolev space. Here, we use the variational methods developed by Szulkin combined with some properties of…
In this paper we study the Kirchhoff problem \begin{equation*} \left \{ \begin{array}{ll} -m(\| u \|^{2})\Delta u = f(u) & \mbox{in $\Omega$,} u=0 & \mbox{on $\partial\Omega$,} \end{array}\right. \end{equation*} in a bounded domain,…
In this paper, we show the existence and multiplicity of nontrivial, non-negative solutions of the fractional $p$-Kirchhoff problem \begin{equation*} \begin{array}{rllll}…
Orlicz-type modules are module analogues of classical Orlicz spaces. We study duality and stable compactness in Orlicz-type modules. We characterize the conditional K\"{o}the dual of an Orlicz-type module as the space of all $\sigma$-order…
We show the existence of a nodal solution with two nodal domains for a generalized Kirchhoff equation of the type $$ -M\left(\displaystyle\int_\Omega \Phi(|\nabla u|)dx\right)\Delta_\Phi u = f(u) \ \ \mbox{in} \ \ \Omega, \ \ u=0 \ \…
In this paper, we first develop the theory of Musielak-Orlicz spaces on locally finite graphs, including completeness, reflexivity, separability, and so on. Then, we give some elementary properties of double phase operators on locally…
In this paper we study double phase problems with nonlinear boundary condition and gradient dependence. Under quite general assumptions we prove existence results for such problems where the perturbations satisfy a suitable behavior in the…
In this paper, we first prove the existence of solutions to Dirichlet problems involving the fractional $g$-Laplacian operator and lower order terms by appealing to sub- and supersolution methods. Moreover, we also state the existence of…
In this article, we investigate the existence and multiplicity of solutions of Kirchhoff equation \begin{equation*} \left\{ \begin{aligned} -(1+b \int_{\mathbb{R}^3}|\nabla u|^2)\Delta u= k(x)\frac{|u|^2 u}{|x|} +\lambda…
In this paper we study logarithmic double phase problems with variable exponents involving nonlinearities that have generalized critical growth. We first prove new continuous and compact embedding results in order to guarantee the…
In this work, we study the existence and multiplicity of solutions for a class of problems involving the $\phi$-Laplacian operator in a bounded domain, where the nonlinearity has a critical growth. The main tool used is the variational…
In this paper we investigate a class of elliptic problems involving a nonlocal Kirchhoff type operator with variable coefficients and data changing its sign. Under appropriated conditions on the coefficients, we have shown existence and…
In this paper we study a class of double phase problems involving critical growth, namely $-\text{div}\big(|\nabla u|^{p-2} \nabla u+ \mu(x) |\nabla u|^{q-2} \nabla u\big)=\lambda|u|^{\vartheta-2}u+|u|^{p^*-2}u$ in $\Omega$ and $u= 0$ on…
In this note we present some recent results for Kirchhoff equations in generalized Gevrey spaces. We show that these spaces are the natural framework where classical results can be unified and extended. In particular we focus on existence…
In this study, we devote our attention to the question of clarifying the existence of a weak solution to a class of quasilinear double-phase elliptic equations with logarithmic convection terms under some appropriate assumptions on data.…
We carry out an investigation of the existence of infinitely many solutions to a fractional $p$-Kirchhoff type problem with a singularity and a superlinear nonlinearity with a homogeneous Dirichlet boundary condition. Further the…