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The paper concerns singular solutions of nonlinear elliptic equations.

Analysis of PDEs · Mathematics 2009-04-21 Luis Caffarelli , YanYan Li , Louis Nirenberg

We establish the existence of infinitely many synchronized solutions for a class of critical Hamiltonian elliptic systems with Hartree-type nonlocal interactions.

Analysis of PDEs · Mathematics 2026-05-22 Weiwei Ye , Minbo Yang

In this paper, we prove multiplicity of solutions for a class of quasilinear problems in $ \mathbb{R}^{N} $ involving variable exponents and nonlinearities of concave-convex type. The main tools used are variational methods, more precisely,…

Analysis of PDEs · Mathematics 2014-09-04 Claudianor O. Alves , José L. P. Barreiro , José V. A. Gonçalves

We prove the existence of infinitely many nonnegative solutions to the following nonlocal elliptic partial differential equation involving singularities \begin{align} (-\Delta)_{p(\cdot)}^{s}…

Analysis of PDEs · Mathematics 2021-08-26 Sekhar Ghosh , Debajyoti Choudhuri , Ratan Kr. Giri

In this paper we prove the existence of infinitely many nontrivial solutions for the class of $(p,\, q)$ fractional elliptic equations involving concave-critical nonlinearities in bounded domains in $\mathbb{R}^N$. Further, when the…

Analysis of PDEs · Mathematics 2019-02-05 Mousomi Bhakta , Debangana Mukherjee

We obtain comparison theorems for non-negative solutions of quasilinear elliptic inequalities

Analysis of PDEs · Mathematics 2010-09-06 Andrej A. Kon'kov

This paper describes infinite sets of polynomial equations in infinitely many variables with the property that the existence of a solution or even an approximate solution for every finite subset of the equations implies the existence of a…

Functional Analysis · Mathematics 2025-03-03 Melvyn B. Nathanson , David A. Ross

In this work, we study the existence and nonexistence of solution for strongly coupled elliptic systems to m-parameters.

Analysis of PDEs · Mathematics 2021-01-05 Felipe Costa , Gil F. de Souza , Marcos Montenegro

In the present work, we establish the existence and multiplicity of positive solutions for the singular elliptic equations with a double weighted nonlocal interaction term defined in the whole space $\mathbb{R}^N$. The nonlocal term and the…

Analysis of PDEs · Mathematics 2025-03-11 Márcia S. B. A. Cardoso , Edcarlos D. Silva , Marcos. L. M. Carvalho , Minbo Yang

In this manuscript we prove the existence of solutions to a fully nonlinear system of (degenerate) elliptic equations of Lane-Emden type and discuss a inhomogeneous generalization.

Analysis of PDEs · Mathematics 2024-04-30 Genival da Silva

In this paper, we study the existence and multiplicity results of nontrivial positive solutions to a quasilinear elliptic equation in $\RN$, when $N\geq2$, as \begin{equation} \Lp…

Analysis of PDEs · Mathematics 2020-03-18 Qi Han

Modelling real world systems frequently requires the solution of systems of nonlinear equations. A number of approaches have been suggested and developed for this computational problem. However, it is also possible to attempt solutions…

Computation · Statistics 2025-01-07 John C. Nash , Ravi Varadhan

A $p$-Laplacian elliptic problem in the presence of both strongly singular and $(p-1)$-superlinear nonlinearities is considered. We employ bifurcation theory, approximation techniques and sub-supersolution method to establish the existence…

Analysis of PDEs · Mathematics 2021-03-16 Carlos Alberto Santos , Jacques Giacomoni , Lais Santos

In this paper we study the multiplicity of positive solutions for nonlinear elliptic equations on $\R^N$. The number of solutions is greater or equal than the number of disjoint intervals on which the nonlinear term is negative.…

Analysis of PDEs · Mathematics 2013-04-12 Claudio Bonanno

In this paper we prove the multiplicity of solutions for a class of quasilinear problems in $ \mathbb{R}^{N} $ involving variable exponents. The main tool used is in the proof are the direct methods, Ekeland's variational principle and some…

Analysis of PDEs · Mathematics 2014-09-02 Claudianor O. Alves , José L. P. Barreiro

In this paper we prove the existence of infinitely many saddle-shaped positive solutions for non-cooperative nonlinear elliptic systems with bistable nonlinearities in the phase-separation regime. As an example, we prove that the system \[…

Analysis of PDEs · Mathematics 2019-11-14 Nicola Soave

Symmetry groups allow to transform solutions of differential equations continuously into other solutions. This property can be used for the observability analysis of infinite-dimensional systems with input and output. In this contribution,…

Optimization and Control · Mathematics 2019-05-28 Bernd Kolar , Markus Schöberl

We demonstrate a kind of linear superposition for a large number of nonlinear equations, both continuum and discrete. In particular, we show that whenever a nonlinear equation admits solutions in terms of Jacobi elliptic functions…

Exactly Solvable and Integrable Systems · Physics 2015-06-15 Avinash Khare , Avadh Saxena

In this work we analyze the existence of solutions to the nonlinear elliptic system: \begin{equation*} \left\{ \begin{array}{rcll} -\Delta u & = & v^q+\a g & \text{in }\Omega , \\ -\Delta v& = &|\nabla u|^{p}+\l f &\text{in }\Omega , \\…

Analysis of PDEs · Mathematics 2017-09-12 Boumediene Abdellaoui , Ahmed Attar , El-Haj Laamri

We consider a class of fully nonlinear second order elliptic equations on Hermitian manifolds closely related to the general notion of $\bfG$-plurisubharmonicity of Harvey-Lawson and an equation treated by Sz\'ekelyhidi-Tosatti-Weinkove in…

Analysis of PDEs · Mathematics 2021-10-04 Mathew George , Bo Guan , Chunhui Qiu