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

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We consider a fractional Schr\"{o}dinger-Poisson system with a general nonlinearity in subcritical and critical case. The Ambrosetti-Rabinowitz condition is not required. By using a perturbation approach, we prove the existence of positive…

Analysis of PDEs · Mathematics 2015-03-31 Jianjun Zhang , João Marcos do Ó , Marco Squassina

In this paper, we study a class of Schr\"{o}dinger-Poisson (SP) systems with general nonlinearity where the nonlinearity does not require Ambrosetti-Rabinowitz and Nehari monotonic conditions. We establish new estimates and explore the…

Analysis of PDEs · Mathematics 2021-09-07 Ching-yu Chen , Tsung-fang Wu

We prove the existence of non-trivial solutions to a system of coupled, nonlinear, Schroedinger equations with general nonlinearity.

Analysis of PDEs · Mathematics 2009-10-01 A. Pomponio , S. Secchi

In this article we present some results on the existence of positive and ground state solutions for the nonlinear Klein-Gordon-Maxwell equations. We introduce a general nonlinearity with subcritical and supercritical growth which does not…

Analysis of PDEs · Mathematics 2012-06-05 Patricia L. Cunha

In this paper we consider the following quasilinear Schr\"odinger-Poisson system in a bounded domain in $\mathbb{R}^{2}$: $$ \left\{ \begin{array}[c]{ll} - \Delta u +\phi u = f(u) &\ \mbox{in } \Omega, -\Delta \phi - \varepsilon^{4}\Delta_4…

Analysis of PDEs · Mathematics 2018-02-22 Giovany M. Figueiredo , Gaetano Siciliano

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

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

In this paper we study a system which is equivalent to a nonlocal version of the well known Brezis Nirenberg problem. The difficulties related with the lack of compactness are here emphasized by the nonlocal nature of the critical nonlinear…

Analysis of PDEs · Mathematics 2016-07-29 Antonio Azzollini , Pietro d'Avenia , Giusi Vaira

We establish the existence of at least one solution to a system of two semilinear coupled Poisson equations with asymptotically linear nonlinearities, without imposing the Ambrosetti-Rabinowitz condition or any of its refinements. The proof…

Analysis of PDEs · Mathematics 2025-09-30 Ablanvi Songo

This work examines a quasilinear Schr\"odinger-Poisson system involving a critical nonlinearity, expressed as \[ -\Delta u + \phi u + \lambda u = |u|^{q-2} u + |u|^4 u, \quad x \in \Omega_r, \] \[ -\Delta \phi - \varepsilon^4 \Delta_4 \phi…

Analysis of PDEs · Mathematics 2026-02-17 Li Chen , Li Wang

In this paper, we are concerned with the ground state solutions of nonlinear fractional Schr\"odinger equation involving critical growth. Without Ambrosetti-Rabinowitz condition and monotonicity condition on the nonlinearity, we get the…

Analysis of PDEs · Mathematics 2016-11-24 Hua Jin , Wenbin Liu

Using variational methods we prove some results about existence and multiplicity of positive bound states of to the following Schr\"odinger-Poisson system: $$ \left\{ \begin{array}{l} \vspace{2mm} -\Delta u+V(x)u+K(x)\phi(x)u=u^5 -\Delta…

Analysis of PDEs · Mathematics 2018-02-08 Giovanna Cerami , Riccardo Molle

In this paper we consider the following quasilinear Schr\"odinger-Poisson system $$ \left\{ \begin{array}[c]{ll} - \Delta u +u+\phi u = \lambda f(x,u)+|u|^{2^{*}-2}u &\ \mbox{in } \mathbb{R}^{3} \\ -\Delta \phi -\varepsilon^{4} \Delta_4…

Analysis of PDEs · Mathematics 2017-07-19 Giovany M. Figueiredo , Gaetano Siciliano

We study a class of critical Schr\"odinger-Poisson system of the form \begin{equation*} \begin{cases} -\Delta u+\lambda V(x)u+\phi u=\mu |u|^{p-2}u+|u|^{4}u& \quad x\in \mathbb{R}^3,\\ -\Delta \phi=u^2&\quad x\in \mathbb{R}^3,\\ \end{cases}…

Analysis of PDEs · Mathematics 2021-12-17 Yongpeng Chen , Zhipeng Yang

In this work we study a system of Schr\"odinger equations involving nonlinearities with quadratic growth. We establish sharp criterion concerned with the dichotomy global existence versus blow-up in finite time. Such a criterion is given in…

Analysis of PDEs · Mathematics 2019-08-13 Norman Noguera , Ademir Pastor

We obtain the existence, nonexistence and multiplicity of positive solutions with prescribed mass for nonlinear Schr\"{o}dinger equations in bounded domains via a global bifurcation approach. The nonlinearities in this paper can be mass…

Analysis of PDEs · Mathematics 2024-09-17 Wei Ji

In the present work we are concerned with the existence of normalized solutions to the following Schr\"odinger-Poisson System $$ \left\{ \begin{array}{ll} -\Delta u + \lambda u + \mu (\ln|\cdot|\ast |u|^{2})u = f(u) \textrm{ \ in \ }…

Analysis of PDEs · Mathematics 2021-07-29 Claudianor O. Alves , Eduardo de S. Boër , Olímpio H. Miyagaki

In this paper we study the existence of ground state solutions for the asymptotically periodic Schr\"odinger-Poisson systems which are coupled by a Schr\"odinger equation of $p$-Laplacian and a Poisson equation of $q$-Laplacian. The method…

Analysis of PDEs · Mathematics 2025-08-26 Yao Du , Linfeng Fan

In this paper we analyze the existence of large positive radial solutions to some quasilinear elliptic systems. Also, a non-radially symmetric solution is obtained by using a lower and upper solution method. The equations are coupled by…

Classical Analysis and ODEs · Mathematics 2011-05-16 Dragos-Patru Covei

We find infinitely many positive non-radial solutions for a system of Schr\"odinger equations with critical growth in a fully attractive or repulsive regime in presence of an external radial trapping potential.

Analysis of PDEs · Mathematics 2022-07-26 Haixia Chen , Angela Pistoia , Giusi Vaira

In this paper we investigate the existence of positive solutions and ground state solution for a class of fractional Schr\"odinger-Poisson equations in $\mathbb R^3$ with general nonlinearities.

Analysis of PDEs · Mathematics 2016-12-15 Ronaldo C. Duarte , Marco A. S. Souto
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