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Related papers: On double phase Kirchhoff problems with singular n…

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We are concerned with the existence and asymptotic behavior of multiple radial sign-changing solutions with the nodal characterization for a Kirchhoff-type problem involving the nonlinearity $|u|^{p-2}u(2<p<4)$ in $\mathbb{R}^3$. By…

Analysis of PDEs · Mathematics 2025-01-23 Haining Fan , Marco Squassina , Jianjun Zhang

The purpose of this paper is to study a class of double phase problems, with a singular term and a superlinear parametric term on the right-hand side. Using the method of Nehari manifold combined with the fibering maps, we prove that for…

Analysis of PDEs · Mathematics 2022-01-05 Ahmed Aberqi , Jaouad Bennouna , Omar Benslimane , Maria Alessandra Ragusa

This paper is concerned with a singular multi-phase problem with variable singularities. The main tool used is the Nehari manifold approach. Existence of at least two positive solutions with positive-negative energy levels are obtained.

Analysis of PDEs · Mathematics 2025-02-17 Mustafa Avci

\noi In this article, we study the existence of non-negative solutions of the following polyharmonic Kirchhoff type problem with critical singular exponential nolinearity $$ \quad \left\{ \begin{array}{lr} \quad…

Analysis of PDEs · Mathematics 2016-04-04 Pawan Kumar Mishra , Sarika Goyal , K. Sreenadh

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 this article, we investigate the existence and multiplicity of solutions of Kirchhoff equation \begin{equation*} \left\{ \begin{aligned} -(1+b \int_{\mathbb{R}^3}|\nabla u|^2)\Delta u= k(x)\frac{|u|^2 u}{|x|} +\lambda…

Analysis of PDEs · Mathematics 2014-12-16 Zupei Shen , Zhiqing Han

In this note, we deal with a problem of the type $$\cases {-h\left ( \int_{\Omega}|\nabla u(x)|^2dx\right ) \Delta u=f(u) & in $\Omega$\cr & \cr u_{|\partial\Omega}=0\ .\cr}$$ As an application of a new general multiplicity result, we…

Analysis of PDEs · Mathematics 2017-10-18 Biagio Ricceri

Using the method of Nehari manifold, we prove the existence of at least two distinct weak solutions to elliptic equation of four order with singulatities and with critical Sobolev growth.

Differential Geometry · Mathematics 2012-10-24 Mohammed Benalili , Kamel Tahri

In this paper, we study certain critical Schr\"{o}dinger-Kirchhoff type systems involving the fractional $p$-Laplace operator on a bounded domain. More precisely, using the properties of the associated functional energy on the Nehari…

Analysis of PDEs · Mathematics 2023-06-16 S. Fareh , K. Akrout , A. Ghanmi , D. D. Repovš

We study Brezis-Nirenberg type problems, governed by the double phase operator $- \mathrm{div}\left(|\nabla u|^{p-2}\, \nabla u + a(x)\, |\nabla u|^{q-2}\, \nabla u\right)$, that involve a critical nonlinearity of the form $|u|^{p^\ast -…

Analysis of PDEs · Mathematics 2024-06-06 Francesca Colasuonno , Kanishka Perera

In this paper, we obtain the existence of weak solutions to the Choquard-Kirchhoff type critical multiphase problem: \begin{equation*} \left\{\begin{array}{cc} &-M(\varphi_{\h}(\lvert{\nabla u}\rvert))div(\lvert{\nabla…

Analysis of PDEs · Mathematics 2025-01-08 Anupma Arora , Gaurav Dwivedi

In this paper we study the following class of nonlocal {problems} involving Caffarelli-Kohn-Nirenberg type critical growth \begin{align*} L(u)&-\lambda h(x)|x|^{-2(1+a)}u=\mu f(x)|u|^{q-2}u+|x|^{-pb}|u|^{p-2}u\;\; \text{in } \mathbb R^N,…

Analysis of PDEs · Mathematics 2019-06-27 Pawan Kumar Mishra , Joao Marcos do Ó , David G. Costa

In this paper we study a singular Finsler double phase problem with a nonlinear boundary condition and perturbations that have a type of critical growth, even on the boundary. Based on variational methods in combination with truncation…

Analysis of PDEs · Mathematics 2021-07-23 Csaba Farkas , Alessio Fiscella , Patrick Winkert

In this paper, we study the following Kirchhoff-Choquard equation $$ -\left(a+b \int_{\mathbb{Z}^3}|\nabla u|^{2} d \mu\right) \Delta u+h(x) u=\left(R_{\alpha}\ast|u|^{p}\right)|u|^{p-2}u,\quad x\in \mathbb{Z}^3, $$ where $a,\,b>0$, $\alpha…

Analysis of PDEs · Mathematics 2024-08-14 Lidan Wang

In this paper we deal with a stationary non-degenerate $p-$Kirchhoff type problem with critical non-linearity and a subcritical parametrized perturbation. We work on bounded domains of the Euclidean space, without any restriction on the…

Analysis of PDEs · Mathematics 2023-05-17 G. N. Cunha , F. Faraci , K. Silva

In this paper, we study two classes of Kirchhoff type problems set on a double phase framework. That is, the functional space where finding solutions coincides with the Musielak-Orlicz-Sobolev space $W^{1,\mathcal H}_0(\Omega)$, with…

Analysis of PDEs · Mathematics 2020-08-04 Alessio Fiscella , Andrea Pinamonti

In this article we study the existence of weak solution, existence of ground state solution using Nehari manifold and existence of infinitely many solutions using Fountain theorem and Dual fountain theorem for a class of doubly nonlocal…

Analysis of PDEs · Mathematics 2020-05-20 Reshmi Biswas , Sweta Tiwari

In this work, we study the higher order Kirchhoff type Choquard equation $(KC)$ involving a critical exponential non-linearity and singular weights. We prove the existence of solution to $(KC)$ using Mountain pass Lemma in light of…

Analysis of PDEs · Mathematics 2019-11-12 R. Arora , J. Giacomoni , T. Mukherjee , K. Sreenadh

In this paper, we apply the method of the Nehari manifold to study the Kirchhoff type equation \begin{equation*} -\Big(a+b\int_\Omega|\nabla u|^2dx\Big)\Delta u=f(x,u) \end{equation*} submitted to Dirichlet boundary conditions. Under a…

Analysis of PDEs · Mathematics 2013-12-20 Cyril Joel Batkam

We study the existence of positive solutions for a class of double phase Dirichlet equations which have the combined effects of a singular term and of a parametric superlinear term. The differential operator of the equation is the sum of a…

Analysis of PDEs · Mathematics 2021-05-17 Nikolaos S. Papageorgiou , Dušan D. Repovš , Calogero Vetro