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Related papers: On critical double phase problems in $\mathbb{R}^N…

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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.…

Analysis of PDEs · Mathematics 2024-01-05 Minh-Phuong Tran , Thanh-Nhan Nguyen

In this paper, we are concerned with the Neumann problem for a class of quasilinear stationary Kirchhoff-type potential systems, which involves general variable exponents elliptic operators with critical growth and real positive parameter.…

Analysis of PDEs · Mathematics 2023-03-06 Nabil Chems Eddine , Dušan D. Repovš

In this paper we are concerned with some abstract results regarding to fractional Orlicz-Sobolev spaces. Precisely, we ensure the compactness embedding for the weighted fractional Orlicz-Sobolev space into the Orlicz spaces, provided the…

Analysis of PDEs · Mathematics 2020-10-21 Edcarlos D. Silva , Marcos L. M. Carvalho , José Carlos de Albuquerque , Sabri Bahrouni

This paper deals with the existence of multiple solutions for the quasilinear equation $-\mathrm{div}\,\mathbf{A}(x,\nabla u)| u| ^{\alpha (x)-2}u=f(x,u)$ in $ \mathbb{R} ^{N}$, which involves a general variable exponent elliptic operator…

Analysis of PDEs · Mathematics 2020-10-12 Xiayang Shi , Vicenţiu D. Rădulescu , Dušan D. Repovš , Qihu Zhang

In this paper we generalize the famous result of [FKS] to the double phase model. In particular, we work with minimal assumptions on the modulating coefficient by introducing a Muckenhoupt-type condition on generalized Orlicz spaces. We…

Analysis of PDEs · Mathematics 2026-01-29 Daviti Adamadze , Lars Diening , Tengiz Kopaliani , Jihoon Ok

In this article we develop a concentration compactness type principle in a variable exponent setup. As an application of this principle we discuss a problem involving fractional `{\it $(p(x),p^+)$-Laplacian}' and power nonlinearities with…

Analysis of PDEs · Mathematics 2021-03-24 Akasmika Panda , Debajyoti Choudhuri

We establish the existence of an entire solution for a class of stationary Schr\"{o}dinger equations with subcritical discontinuous nonlinearity and lower bounded potential that blows-up at infinity. The abstract framework is related to…

Analysis of PDEs · Mathematics 2007-05-23 Teodora Liliana Dinu

We establish two global boundedness results for weak solutions to generalized Schr\"{o}dinger-type double phase problems with variable exponents in $\mathbb{R}^N$ under new critical growth conditions optimally introduced in [26, 32]. More…

Analysis of PDEs · Mathematics 2026-04-23 Hoang Hai Ha , Ky Ho , Bui The Quan , Inbo Sim

We are concerned with the two-power nonlinear Schr\"odinger-type equations with non-local terms. We consider the framework of Sobolev-Lorentz spaces which contain singular functions with infinite-energy. Our results include global…

Analysis of PDEs · Mathematics 2019-10-02 Vanessa Barros , Lucas C. F. Ferreira , Ademir Pastor

In this paper we prove a Lions type result for a large class of Orlicz-Sobolev space that can be nonreflexive and use this result to show the existence of solution for a large class of quasilinear problem on a nonreflexive Orlicz-Sobolev…

Analysis of PDEs · Mathematics 2021-02-12 Claudianor O. Alves , Marcos L. Carvalho

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…

Analysis of PDEs · Mathematics 2015-04-06 Jefferson A. Santos

In this paper, we develop some properties of the $a_{x,y}(\cdot)$-Neumann derivative for the nonlocal $s(\cdot,\cdot)$-order operator in fractional Musielak-Sobolev spaces with variable $s(\cdot,\cdot)-$order. Therefore we prove the basic…

Analysis of PDEs · Mathematics 2024-12-17 Mohammed Srati

In this paper, we study the existence of solutions for the new fractinal Robin equations with variable exponents. Moreover, we deal with the logarithm-type nonlinearity. In particular, we consider two cases: critical and subcritical cases.

Analysis of PDEs · Mathematics 2022-11-23 Reshmi Biswas , Anouar Bahrouni , Alessio Fiscella

Study the following two-component elliptic system% \begin{equation*} \left\{\aligned&\Delta u-(\lambda a(x)+a_0)u+u^3+\beta v^2u=0\quad&\text{in }\bbr^4,\\% &\Delta v-(\lambda b(x)+b_0)v+v^3+\beta u^2v=0\quad&\text{in }\bbr^4,\\%…

Analysis of PDEs · Mathematics 2015-06-11 Yuanze Wu , Wenming Zou

We establish theorems on the existence and compactness of solutions to the $\sigma_2$-Nirenberg problem on the standard sphere $\mathbb S^2$. A first significant ingredient, a Liouville type theorem for the associated fully nonlinear…

Analysis of PDEs · Mathematics 2021-08-06 YanYan Li , Han Lu , Siyuan Lu

This paper deals with some classes of Kirchhoff type problems on a double phase setting and with nonlinear boundary conditions. Under general assumptions, we provide multiplicity results for such problems in the case when the perturbations…

Analysis of PDEs · Mathematics 2021-12-16 Alessio Fiscella , Greta Marino , Andrea Pinamonti , Simone Verzellesi

In this paper, we consider the multiplicity of solutions for a class of Kirchhoff type problems with sub-linear and critical terms on an unbounded domain. With the aid of Ekeland's variational principle and the concentration compactness…

Functional Analysis · Mathematics 2016-05-23 Xiaofei Cao , Junxiang Xu , Jun Wang

In our series of papers, we establish infinite concentration and oscillation estimates for supercritical semilinear elliptic equations in discs. Especially, we extend the previous result by the author (N. arXiv:2404.01634) to the general…

Analysis of PDEs · Mathematics 2025-07-08 Daisuke Naimen

The main goal this work is to prove two results like Strauss and Lions for Orlicz-Sobolev spaces. After, we use these results for study the existence of solutions for a class of quasilinear problems in $\mathbb{R}^{N}$.

Analysis of PDEs · Mathematics 2014-01-28 Claudianor O. Alves , Giovany M. Figueiredo , Jefferson A. Santos

We prove the multiplicity and concentration of normalized solutions of critical biharmonic equations with combined nonlinearities in $\mathbb{R}^{N}$ \begin{equation*} \Delta^{2}u+V(\varepsilon x)u=\lambda u+\mu |u|^{q-2}u+|u|^{2^{**}-2}u…

Analysis of PDEs · Mathematics 2026-03-02 Yueqiang Song , Jiaying Ma , Dušan D. Repovš