Some Inclusion Properties for Meromorphic Functions Defined by New Generalization of Mittag-Leffler Function

In this paper, the authors introduced a new operator by using a generalized Mittag-Leffler function. Also, the authors defined the meromorphic subclasses associated. Finally calculated inclusion relation

On the Steklov problem involving the p(x)-Laplacian with indefinite weight

Under suitable assumptions, we study the existence of a weak nontrivial solution for the following Steklov problem involving the $p(x)$-Laplacian $$\begin{cases}\Delta_{p(x)}u=a(x)|u|^{p(x)-2}u \quad \text{in }\Omega, \\ |\nabla u|^{p(x)-2}\frac{\partial u}{\partial \nu}=\lambda V(x)|u|^{q(x)-2}u \quad \text{on }\partial \Omega.\end{cases}$$ Our approach is based on min-max method and Ekeland's variational principle

Min-max method for some classes of Kirchhoff problems involving the ψ \psi -Hilfer fractional derivative

In this work, we develop some variational settings related to some singular $p$-Kirchhoff problems involving the $\psi$-Hilfer fractional derivative. More precisely, we combine the variational method with the min-max method in order to prove the existence of nontrivial solutions for the given problem. Our main result generalizes previous ones in the literature

Nehari manifold and multiplicity result for elliptic equation involving p-laplacian problems

This article shows the existence and multiplicity of positive solutions of the $p$-Laplacien problem \displaystyle -\Delta_{p} u=\frac{1}{p^{\ast}}\frac{\partial F(x,u)}{\partial u} + \lambda a(x)|u|^{q-2}u \quad \mbox{for } x\in\Omega;\quad \quad u=0,\quad \mbox{for } x\in\partial\Omega where $\Omega$ is a bounded open set in $\mathbb{R}^n$ with smooth boundary, $1<q<p<n$, $p^{\ast}=\frac{np}{n-p}$, $\lambda \in \mathbb{R}\backslash \{0\}$ and $a$ is a smooth function which may change sign in $\overline{\Omega}$. The method is based on Nehari results on three sub-manifolds of the space $W_{0}^{1,p}$

Nonlocal ▫pp▫-Kirchhoff equations with singular and critical nonlinearity terms

The objective of this work is to investigate a nonlocal problem involving singular and critical nonlinearities: ▫begin{cases} ([u]_{s,p}^p)^{sigma-1}(-Delta)^s_p u = frac{lambda}{u^{gamma}}+u^{ p_s^{*}-1} & quad text{in }Omega,\ u>0, & quad text{in }Omega,\ u=0, & quad text{in }mathbb{R}^{N}setminus Omega, end{cases}▫ where ▫$Omega$▫ is a bounded domain in ▫$mathbb{R}^N$▫ with the smooth boundary ▫$partial Omega$▫, ▫$0 sp$, $1<sigma<p^*_s/p,$▫ with ▫$p_s^{*}=frac{Np}{N-ps},$▫ ▫$(- Delta )_p^s$▫ is the nonlocal ▫$p$▫-Laplace operator and ▫$[u]_{s,p}$▫ is the Gagliardo $p$-seminorm. We combine some variational techniques with a truncation argument in order to show the existence and the multiplicity of positive solutions to the above problem

Multiplicity results for fractional Schrödinger-Kirchhoff systems involving critical nonlinearities

In this article, we study certain critical Schrödinger-Kirchhoff-type systems involving the fractional $p$-Laplace operator on a bounded domain. More precisely, using the properties of the associated functional energy on the Nehari manifold sets and exploiting the analysis of the fibering map, we establish the multiplicity of solutions for such systems

Existence of solutions for fractional differential equations with Dirichlet boundary conditions

In this article, we apply the Nehari manifold to prove the existence of a solution of the fractional differential equation \displaylines{ \frac{d}{dt} \Big(\frac12 {\,}_0D_t^{-\beta}(u'(t)) +\frac12 {\,}_tD_T^{-\beta}(u'(t)))= f(t,u(t)) + \lambda h(t)|u(t)|^{r-2}u(t), \cr \text{a.e } t\in [0,T],\cr u(0)=u(T)=0, } where _0D_t^{-\beta},\; _tD_T^{-\beta} are the left and right Riemann-Liouville fractional integrals, respectively, of order $0< \beta < 1$

Multiplicity results for fractional Schrödinger-Kirchhoff systems involving critical nonlinearities

In this article, we study certain critical Schrödinger-Kirchhoff-type systems involving the fractional pp-Laplace operator on a bounded domain. More precisely, using the properties of the associated functional energy on the Nehari manifold sets and exploiting the analysis of the fibering map, we establish the multiplicity of solutions for such systems