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Related papers: Schr\"odinger-Poisson systems with a general criti…

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We consider a class of noncooperative Schr\"{o}dinger-Kirchhoff type system which involves a general variable exponent elliptic operator with critical growth. Under certain suitable conditions on the nonlinearities, we establish the…

Analysis of PDEs · Mathematics 2024-06-17 N. Chems Eddine , D. D. Repovš

We find infinitely many positive non-radial solutions for a nonlinear Schrodinger-Poisson system.

Analysis of PDEs · Mathematics 2010-06-04 Pietro d'Avenia , Alessio Pomponio , Giusi Vaira

In this paper, we consider the final state problem for the nonlinear Schr\"odinger equation with a homogeneous nonlinearity which is of the long range critical order and is not necessarily a polynomial, in one and two space dimensions. As…

Analysis of PDEs · Mathematics 2016-12-15 Satoshi Masaki , Hayato Miyazaki

We establish some existence results for Schr\"odinger $p(x)$-Laplace equations in $\mathbb{R}^N$ with various potentials and critical growth of nonlinearity that may occur on some nonempty set, although not necessarily the whole space…

Analysis of PDEs · Mathematics 2018-07-12 Ky Ho , Yun-Ho Kim , Inbo Sim

In this paper, we consider the nonlinear Schr\"odinger equation with the super critical power of nonlinearity in the attractive case. We give a sufficient condition and a necessary condition to obtain global or blowing up solutions. These…

Analysis of PDEs · Mathematics 2012-07-10 Pascal Bégout

We prove the existence of a ground state positive solution of Schr\"odinger-Poisson systems in the plane of the form $$ -\Delta u + V(x)u + \frac{\gamma}{2\pi} \left(\log|\cdot| \ast u^2 \right)u = b |u|^{p-2}u \qquad\text{in}\…

Analysis of PDEs · Mathematics 2022-06-07 Riccardo Molle , Andrea Sardilli

We provide an existence result for a Schr\"odinger-Poisson system in gradient form, set in the whole plane, in the case of zero mass. Since the setting is limiting for the Sobolev embedding, we admit nonlinearities with subcritical or…

Analysis of PDEs · Mathematics 2025-07-23 Federico Bernini , Giulio Romani , Cristina Tarsi

We investigate the existence, non-existence, and multiplicity of positive solutions to a class of quasilinear Schrodinger equations with a prescribed mass condition in higher dimensions. Using the dual approach, the equation is transformed…

Analysis of PDEs · Mathematics 2024-11-26 Ayesha Baig , Li Zhouxin

We establish the existence of an entire solution for a class of stationary Schr\"{o}dinger systems with subcritical discontinuous nonlinearities and lower bounded potentials that blow-up at infinity. The proof is based on the critical point…

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

We study the existence of positive solutions for a class of systems which strongly couple a quasilinear Schr\"odinger equation driven by a weighted $N$-Laplace operator and without the mass term, and a higher-order fractional Poisson…

Analysis of PDEs · Mathematics 2025-07-23 Giulio Romani

We consider the following Schr\"odinger-Bopp-Podolsky system with critical and sublinear terms \begin{equation*} \begin{cases} - \Delta u+ u+Q(x)\phi u= \vert u\vert^4 u+ \lambda K(x)\vert u \vert^{p-1}u&\mbox{ in }\ \mathbb{R}^3 \smallskip…

Analysis of PDEs · Mathematics 2025-07-28 Heydy M. Santos Damian , Gaetano Siciliano

The present study is concerned with the following Schr\"{o}dinger-Poisson system involving critical nonlocal term $$ \left\{ \begin{array}{ll} -\Delta u+u-K(x)\phi |u|^3u=\lambda f(x)|u|^{q-2}u, & x\in\mathbb{R}^3, -\Delta \phi=K(x)|u|^5, &…

Analysis of PDEs · Mathematics 2017-03-20 Liejun Shen , Xiaohua Yao

In this paper we study a mixed problem for the nonlinear Schr\"odinger equation globally that have a nonlinear adding, in which the coefficient is a generalized function. Here is proved a global solvability theorem of the considered problem…

Mathematical Physics · Physics 2012-11-16 Kamal N. Soltanov

In this paper, we study the existence of multiple positive solutions for a class of fractional Schr\"{o}dinger-Poisson systems involving sign-changing potential and critical nonlinearities on an unbounded domain. With the help of Nehari…

Analysis of PDEs · Mathematics 2021-03-03 Haining Fan , Zhaosheng Feng , Xingjie Yan

This paper is devoted to the study of the existence of positive and bounded solutions for a Schr\"odinger type equation defined on the entire Euclidean space, involving a general integro-differential operator. We consider the case where the…

Analysis of PDEs · Mathematics 2026-04-10 Ronaldo C. Duarte , Diego Ferraz

We consider the existence of ground state solutions for a class of zero-mass Chern-Simons-Schr\"{o}dinger systems \[ \left\{ \begin{array}{ll} \displaystyle -\Delta u +A_0 u+\sum\limits_{j=1}^2A_j^2 u=f(u)-a(x)|u|^{p-2}u, \newline…

Analysis of PDEs · Mathematics 2024-03-28 Liejun Shen , Marco Squassina

The Cauchy problem for the semi-relativistic Schr\"odinger-Poisson system of equations is studied in ${\mathbb R}^n$, $n\geq 1$, for a wide class of nonlocal interactions. Furthermore, the asymptotic behavior of the solution as the mass…

Mathematical Physics · Physics 2012-12-24 Walid Abou Salem , Thomas Chen , Vitali Vougalter

We prove the existence of infinitely many high energy sign-changing solutions for some classes of Schrodinger-Poisson systems in bounded domains, with nonlinearities having subcritical or critical growth. Our approach is variational and…

Analysis of PDEs · Mathematics 2015-01-27 Cyril Joel Batkam

In this paper, we study the Schr\"odinger-Poisson system $$ \left \{ \begin{array}{l} -\Delta u=\sqrt{p}u^{p-1}v, \quad u>0 \quad in \quad R^n, -\Delta v=\sqrt{p}u^p, \quad v>0 \quad in \quad R^n \end{array} \right. $$ with $n \geq 3$ and…

Analysis of PDEs · Mathematics 2014-11-07 Yutian Lei

We generalize a theorem of Lair concerning the existence of positive entire large solutions to competitive semilinear elliptic systems. While Lair's original result \cite{Lair2025} was established for power-type nonlinearities, our work…

Analysis of PDEs · Mathematics 2025-11-21 Dragos-Patru Covei