Shengda Zeng
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View article: Superlinear perturbations of a double‐phase eigenvalue problem
Superlinear perturbations of a double‐phase eigenvalue problem Open
We consider a perturbed version of an eigenvalue problem for the double‐phase operator. The perturbation is superlinear, but need not satisfy the Ambrosetti–Robinowitz condition. Working on the Sobolev–Orlicz space with for and using varia…
View article: Double phase elliptic inclusions with convection and logarithmic perturbed terms
Double phase elliptic inclusions with convection and logarithmic perturbed terms Open
This paper deals with a new double phase elliptic inclusion (DPEI) formulated by a double phase partial differential operator with logarithmic perturbation, a general multivalued convection term defined in the domain and a general multival…
View article: Dirichlet problems with unbalanced growth and double resonance
Dirichlet problems with unbalanced growth and double resonance Open
We consider a nonlinear, nonhomogeneous Dirichlet problem driven by a nonautonomous (p,2) -Laplacian with unbalanced growth. The reaction is resonant both at \pm\infty and at zero (double resonance). Using variational tools together with t…
View article: Anisotropic Double Phase Elliptic Inclusion Systems with Logarithmic Perturbation and Multivalued Convections
Anisotropic Double Phase Elliptic Inclusion Systems with Logarithmic Perturbation and Multivalued Convections Open
In this paper, we investigate a class of variable exponent double phase elliptic inclusion systems involving anisotropic partial differential operators with logarithmic perturbation as well as two fully coupled multivalued terms, one of th…
View article: A class of nonlinear double-phase Dirichlet fractional differential equations
A class of nonlinear double-phase Dirichlet fractional differential equations Open
In this paper, we study the existence of positive solutions for a new class of double-phase Dirichlet fractional differential equations with singular and superlinear terms. By applying the Nehari manifold method we show that for all small …
View article: Differential inclusion systems with fractional competing operator and multivalued fractional convection term
Differential inclusion systems with fractional competing operator and multivalued fractional convection term Open
In this work, the existence of solutions (in a suitable sense) to a family of inclusion systems involving fractional, possibly competing, elliptic operators, fractional convection, and homogeneous Dirichlet boundary conditions is establish…
View article: Differential inclusion systems with double phase competing operators, convection, and mixed boundary conditions
Differential inclusion systems with double phase competing operators, convection, and mixed boundary conditions Open
In this paper, a new framework for studying the existence of generalized or strongly generalized solutions to a wide class of inclusion systems involving double-phase, possibly competing differential operators, convection, and mixed bounda…
View article: Existence results of variable exponent double-phase multivalued elliptic inequalities with logarithmic perturbation and convections
Existence results of variable exponent double-phase multivalued elliptic inequalities with logarithmic perturbation and convections Open
In this study, we deal with a multivalued elliptic variational inequality involving a logarithmic perturbed variable exponents double-phase operator. Additionally, it features a multivalued convection term alongside two multivalued terms, …
View article: AN IMPLICIT DIFFERENCE METHOD FOR SOLVING COUPLED MOBILE/IMMOBILE TRANSPORT SYSTEMS WITH GENERALIZED TIME-FRACTIONAL OPERATORS
AN IMPLICIT DIFFERENCE METHOD FOR SOLVING COUPLED MOBILE/IMMOBILE TRANSPORT SYSTEMS WITH GENERALIZED TIME-FRACTIONAL OPERATORS Open
This paper introduces an implicit difference scheme for solving a specific class of coupled mobile/immobile transport systems involving generalized time-fractional operators, in which we discretize the derivative with respect to time using…
View article: Doubling measure and regularity to <i>K</i> -quasiminimizers of double-phase energy
Doubling measure and regularity to <i>K</i> -quasiminimizers of double-phase energy Open
We consider an integral functional involving the double-phase operator in a metric measure space equipped with a doubling measure. On the basis of suitable hypotheses on the function governing the phase changes, we design a unifying approa…
View article: Indefinite perturbations of an unbalanced growth eigenvalue problem
Indefinite perturbations of an unbalanced growth eigenvalue problem Open
We consider indefinite perturbations of a double-phase eigenvalue problem. The perturbation is sublinear or superlinear, and it is in general sign-changing. Using the Nehari manifold, we prove the existence of two constant sign solutions f…
View article: Fractional elliptic obstacle systems with multivalued terms and nonlocal operators
Fractional elliptic obstacle systems with multivalued terms and nonlocal operators Open
In this paper, we introduce and study a fractional elliptic obstacle system, which is composed of two elliptic inclusions with fractional (pi, qi)-Laplace operators, nonlocal functions, and multivalued terms. The weak solution of fractiona…
View article: A generalized penalty method for quasi-variational-hemivariational inequalities
A generalized penalty method for quasi-variational-hemivariational inequalities Open
In this paper we investigate the existence of solutions for a class of set-valued quasi-variational-hemivariational inequalities in a real reflexive Banach space. We employ the theory of Brézis pseudomonotone operators combined with a gene…
View article: Multiple Positive Solutions for Quasilinear Elliptic Problems in Expanding Domains
Multiple Positive Solutions for Quasilinear Elliptic Problems in Expanding Domains Open
In this paper we prove the existence of multiple positive solutions for a quasilinear elliptic problem with unbalanced growth in expanding domains by using variational methods and the Lusternik–Schnirelmann category theory. Based on the pr…
View article: A new class of evolution multivalued quasi-variational inequalities I: existence and nonsmooth optimal control
A new class of evolution multivalued quasi-variational inequalities I: existence and nonsmooth optimal control Open
In this paper, we consider a new kind of evolution multivalued quasi-variational inequalities with feedback effect and a nonlinear bifunction which contain several (evolution) quasi-variational/hemivariational inequalities as special cases…
View article: Infinitely many small energy solutions to the <inline-formula><tex-math id="M1">$ p $</tex-math></inline-formula>-Laplacian problems of Kirchhoff type with Hardy potential
Infinitely many small energy solutions to the -Laplacian problems of Kirchhoff type with Hardy potential Open
The present paper is devoted to obtaining the multiplicity result of solutions to the nonlinear elliptic equations of Kirchhoff type with Hardy potential. More precisely, the main purpose of this paper, under certain assumptions on the Kir…
View article: Nonlocal Double Phase Implicit Obstacle Problems with Multivalued Boundary Conditions
Nonlocal Double Phase Implicit Obstacle Problems with Multivalued Boundary Conditions Open
<p>In this paper, we consider a mixed boundary value problem with a nonhomogeneous, nonlinear differential operator (called double phase operator), a nonlinear convection term (a reaction term depending on the gradient), th…
View article: Variational–hemivariational system for contaminant convection–reaction–diffusion model of recovered fracturing fluid
Variational–hemivariational system for contaminant convection–reaction–diffusion model of recovered fracturing fluid Open
This work is devoted to study the convection–reaction–diffusion behavior of contaminant in the recovered fracturing fluid which flows in the wellbore from shale gas reservoir. First, we apply various constitutive laws for generalized non-N…
View article: Editorial: Overview and Some New Directions
Editorial: Overview and Some New Directions Open
The Special Issue contains eleven accepted and published submissions to a Special Issue of the MDPI journal Axioms on the subject of “Nonlinear Dynamical Systems with Applications” [...]
View article: Existence results for Dirichlet double phase differential inclusions
Existence results for Dirichlet double phase differential inclusions Open
"In this paper we consider a class of double phase differential inclusions of the type $$\left\{ \begin{array}{ll} -{\rm div\;}\left(|\nabla u|^{p-2}\nabla u+\mu(x)|\nabla u|^{q-2}\nabla u\right) \in \partial_C^2 f(x,u) , & \mbox{ in }\Ome…