25 citations · 65 across the 40 of their papers we have counts for
49 papers · 1 filter
Hölder regularity for logarithmic double phase problems
Ky Ho, Yun-Ho Kim, Patrick Winkert
We investigate boundedness and regularity properties of weak solutions to a class of generalized logarithmic double phase equations with variable exponents. The considered operator…
Mixed double phase equations with local and nonlocal operators
Anupma Arora, Shilpa Gupta, Patrick Winkert
In this paper, we study a new class of mixed double phase problems that combine local and nonlocal operators. We consider two different models. The first model is driven by the fra…
Critical double phase problems involving sandwich-type nonlinearities
Csaba Farkas, Alessio Fiscella, Ky Ho +1
In this paper we study problems with critical and sandwich-type growth represented by \begin{align*} -\operatorname{div}\Big(|\nabla u|^{p-2}\nabla u + a(x)|\nabla u|^{q-2}\nabla u…
Logarithmic double phase problems with generalized critical growth
Rakesh Arora, Ángel Crespo-Blanco, Patrick Winkert
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 c…
Degenerate singular Kirchhoff problems in Musielak-Orlicz spaces
Umberto Guarnotta, Patrick Winkert
In this paper we study quasilinear elliptic Kirchhoff equations driven by a non-homogeneous operator with unbalanced growth and right-hand sides that consist of sub-linear, possibl…
Double phase problems with variable exponents depending on the solution and the gradient in the whole space
Ala Eddine Bahrouni, Anouar Bahrouni, Patrick Winkert
In this paper, we establish continuous and compact embeddings for a new class of Musielak-Orlicz Sobolev spaces in unbounded domains driven by a double phase operator with variable…
On singularly perturbed -Laplace Schrödinger equation with logarithmic nonlinearity
Deepak Kumar Mahanta, Tuhina Mukherjee, Patrick Winkert
This article focuses on the study of the existence, multiplicity and concentration behavior of ground states as well as the qualitative aspects of positive solutions for a …
Degenerate Kirchhoff problems with nonlinear Neumann boundary condition
Franziska Borer, Marcos T. O. Pimenta, Patrick Winkert
In this paper we consider degenerate Kirchhoff-type equations of the form \[-ϕ(Ξ(u)) \left(\mathcal{A}(u)-|u|^{p-2}u\right) = f(x,u)\quad \text{in } Ω,\] \[\phantom{aaiaaaaaaaaa}ϕ(…
Elliptic -Laplacian systems with nonlinear boundary condition
Franziska Borer, Siegfried Carl, Patrick Winkert
In this paper we study quasilinear elliptic systems given by \begin{equation*} \begin{aligned} -Δ_{p_1}u_1 & =-|u_1|^{p_1-2}u_1 \quad && \text{in } Ω,\newline -Δ_{p_2}u_2 & =-|u_2|…
Least energy sign-changing solution for degenerate Kirchhoff double phase problems
Ángel Crespo-Blanco, Leszek Gasiński, Patrick Winkert
In this paper we study the following nonlocal Dirichlet equation of double phase type \begin{align*} -ψ\left [ \int_Ω\left ( \frac{|\nabla u |^p}{p} + μ(x) \frac{|\nabla u|^q}{q}\r…
On logarithmic double phase problems
Rakesh Arora, Ángel Crespo-Blanco, Patrick Winkert
In this paper we introduce a new logarithmic double phase type operator of the form\begin{align*}\mathcal{G}u:=-\operatorname{div}\left(|\nabla u|^{p(x)-2}\nabla u+μ(x)\left[\log(e…
Superlinear elliptic equations with unbalanced growth and nonlinear boundary condition
Eleonora Amoroso, Ángel Crespo-Blanco, Patrizia Pucci +1
In this paper we first introduce an innovative equivalent norm in the Musielak-Orlicz Sobolev spaces in a very general setting and we then present a new result on the boundedness o…
Nehari manifold approach for superlinear double phase problems with variable exponents
Ángel Crespo-Blanco, Patrick Winkert
In this paper we consider quasilinear elliptic equations driven by the variable exponent double phase operator with superlinear right-hand sides. Under very general assumptions on…
Existence of ground state solutions for a Choquard double phase problem
Rakesh Arora, Alessio Fiscella, Tuhina Mukherjee +1
In this paper we study quasilinear elliptic equations driven by the double phase operator involving a Choquard term of the form \begin{align*} -\mathcal{L}_{p,q}^{a}(u) + |u|^{p-2}…
Infinitely many solutions to Kirchhoff double phase problems with variable exponents
Ky Ho, Patrick Winkert
In this work we deal with elliptic equations driven by the variable exponent double phase operator with a Kirchhoff term and a right-hand side that is just locally defined in terms…
The sub-supersolution method for variable exponent double phase systems with nonlinear boundary conditions
Umberto Guarnotta, Roberto Livrea, Patrick Winkert
In this paper we study quasilinear elliptic systems driven by variable exponent double phase operators involving fully coupled right-hand sides and nonlinear boundary conditions. T…
New embedding results for double phase problems with variable exponents and a priori bounds for corresponding generalized double phase problems
Ky Ho, Patrick Winkert
In this paper we present new embedding results for Musielak-Orlicz Sobolev spaces of double phase type. Based on the continuous embedding of into $L^{\mathca…
Multi-valued variational inequalities for variable exponent double phase problems: comparison and extremality results
Siegfried Carl, Vy Khoi Le, Patrick Winkert
We prove existence and comparison results for multi-valued variational inequalities in a bounded domain of the form \begin{equation*} u\in K\,:\, 0 \in Au+\partial I_K(u)+\math…
On double phase Kirchhoff problems with singular nonlinearity
Rakesh Arora, Alessio Fiscella, Tuhina Mukherjee +1
In this paper, we study multiplicity results for double phase problems of Kirchhoff type with right-hand sides that include a parametric singular term and a nonlinear term of subcr…
Double phase implicit obstacle problems with convection and multivalued mixed boundary value conditions
Shengda Zeng, Vicenţiu D. Rădulescu, Patrick Winkert
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 react…
On a class of critical double phase problems
Csaba Farkas, Alessio Fiscella, Patrick Winkert
In this paper we study a class of double phase problems involving critical growth, namely $-\text{div}\big(|\nabla u|^{p-2} \nabla u+ μ(x) |\nabla u|^{q-2} \nabla u\big)=λ|u|^{\var…
Parametric superlinear double phase problems with singular term and critical growth on the boundary
Ángel Crespo-Blanco, Nikolaos S. Papageorgiou, Patrick Winkert
In this paper we study quasilinear elliptic equations driven by the double phase operator along with a reaction that has a singular and a parametric superlinear term and with a non…
Double phase obstacle problems with multivalued convection and mixed boundary value conditions
Shengda Zeng, Vicenţiu D. Rădulescu, Patrick Winkert
In this paper, we consider a mixed boundary value problem with a double phase partial differential operator, an obstacle effect and a multivalued reaction convection term. Under ve…
Combined effects of singular and superlinear nonlinearities in singular double phase problems in
Wulong Liu, Patrick Winkert
This paper is concerned with multiplicity results for parametric singular double phase problems in via the Nehari manifold approach. It is shown that the problem und…