Results 61 to 70 of about 33,794 (182)

Normalized solutions for critical Schrödinger equations involving (2,q)-Laplacian [PDF]

Opuscula Mathematica
In this paper, we consider the following critical Schrödinger equation involving \((2,q)\)-Laplacian: \[\begin{cases} -\Delta u-\Delta_{q} u=\lambda u+\mu |u|^{\gamma-2}u+|u|^{2^*-2}u \quad\text{in }\mathbb{R}^N, \\ \int_{\mathbb{R}^N} |u|^{2}dx=a^2,\end{
Lulu Wei, Yueqiang Song
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Existence of multiple solutions for a quasilinear Neumann problem with critical exponent

Boundary Value Problems, 2018
The main purpose of this paper is to establish the existence and multiplicity of nontrivial solutions for a quasilinear Neumann problem with critical exponent.
Yuanxiao Li, Suxia Xia
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Multiplicity of solutions to a p-Kirchhoff equation with critical exponent

Boundary Value Problems
In this paper, we consider the following p-Kirchhoff equation: P { [ M ( ∥ u ∥ p ) ] p − 1 ( − Δ p u + | u | p − 2 u ) = λ f ( x , u ) + | u | p ∗ − 2 u in Ω , u = 0 , on ∂ Ω , $$ \left \{ \textstyle\begin{array}{l@{\quad}l} [M(\|u\|^{p})]^{p-1}\left ...
Zhaomin Jiang
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Infinitely many solutions for the p-fractional Kirchhoff equations with electromagnetic fields and critical nonlinearity

Nonlinear Analysis, 2018
In this paper, we consider the fractional Kirchhoff equations with electromagnetic fields and critical nonlinearity. By means of the concentration-compactness principle in fractional Sobolev space and the Kajikiya's new version of the symmetric mountain ...
Sihua Liang, Jihui Zhang
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Fractional elliptic problems with two critical Sobolev-Hardy exponents

Electronic Journal of Differential Equations, 2018
By using the mountain pass lemma and a concentration compactness principle, we obtain the existence of positive solutions to the fractional elliptic problem with two critical Hardy-Sobolev exponents at the origin.
Wenjing Chen
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Multiplicity of solutions for quasilinear elliptic problems involving $\Phi$-Laplacian operator and critical growth

Electronic Journal of Qualitative Theory of Differential Equations, 2019
In this paper, we study a class of quasilinear elliptic equations with $\Phi$-Laplacian operator and critical growth. Using the symmetric mountain pass theorem and the concentration-compactness principle, we demonstrate that there exists $\lambda_i>0 ...
Xuewei Li, Gao Jia
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Nonlinear boundary value problems of a class of elliptic equations involving critical variable exponents

Boundary Value Problems, 2019
In this paper, we first obtain the existence of solutions for a class of elliptic equations involving critical variable exponents and nonlinear boundary values by the mountain pass theorem and concentration compactness principle.
Yingying Shan, Yongqiang Fu
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The Compact Embeddings and the Concentration-Compactness Principles for Anisotropic Variable Exponent Sobolev Spaces and Applications

The Journal of Geometric Analysis
Abstract In this paper, we present new results about the compact embeddings of anisotropic variable exponent Sobolev spaces into variable Lebesgue spaces. We also refine and extend the concentration–compactness principle to trace embeddings in these spaces.
Nabil Chems Eddine, Maria Alessandra Ragusa   +1 more
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Existence of positive solutions to Kirchhoff type problems involving singular and critical nonlinearities

Electronic Journal of Differential Equations, 2018
In this study, we study a Kirchhoff type problem involving singular and critical nonlinearities. With aid of variational methods and concentration compactness principle, we prove that the problem admits a weak solution.
Chun-Yu Lei, Gao-Sheng Liu
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Existence of solutions for p-Laplacian equations with electromagnetic fields and critical nonlinearity

Electronic Journal of Differential Equations, 2015
In this article, we study the perturbed p-Laplacian equation problems with critical nonlinearity in R^N. By using the concentration compactness principle and variational method, we establish the existence and multiplicity of nontrivial solutions of ...
Zhongyi Zhang
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