Results 1 to 10 of about 15,857,552 (384)

Multiple solutions of Kirchhoff type equations involving Neumann conditions and critical growth

AIMS Mathematics, 2021
In this paper, we consider a Neumann problem of Kirchhoff type equation \begin{equation*} \begin{cases} \displaystyle-\left(a+b\int_{\Omega}|\nabla u|^2dx\right)\Delta u+u= Q(x)|u|^4u+\lambda P(x)|u|^{q-2}u, &\rm \mathrm{in}\ \ \Omega ...
Jun Lei, Hongmin Suo
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On sufficient “local” conditions for existence results to generalized p(.)-Laplace equations involving critical growth

Advances in Nonlinear Analysis, 2022
In this article, we study the existence of multiple solutions to a generalized p(⋅)p\left(\cdot )-Laplace equation with two parameters involving critical growth.
Ho Ky, Sim Inbo
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Existence of nontrivial solutions for critical Kirchhoff-Poisson systems in the Heisenberg group

Advanced Nonlinear Studies, 2022
This article is devoted to the study of the combined effects of logarithmic and critical nonlinearities for the Kirchhoff-Poisson system −M∫Ω∣∇Hu∣2dξΔHu+μϕu=λ∣u∣q−2uln∣u∣2+∣u∣2uinΩ,−ΔHϕ=u2inΩ,u=ϕ=0on∂Ω,\left\{\begin{array}{ll}-M\left(\mathop ...
Pucci Patrizia, Ye Yiwei
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Existence and Concentration Behavior of Solutions of the Critical Schrödinger–Poisson Equation in ${\mathbb{R}}^3$

Mathematics, 2021
In this paper, we study the singularly perturbed problem for the Schrödinger–Poisson equation with critical growth. When the perturbed coefficient is small, we establish the relationship between the number of solutions and the profiles of the ...
Jichao Wang, Ting Yu
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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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Fourth-order elliptic problems with critical nonlinearities by a sublinear perturbation

Nonlinear Analysis, 2021
In this paper, we get the existence of two positive solutions for a fourth-order problem with Navier boundary condition. Our nonlinearity has a critical growth, and the method is a local minimum theorem obtained by Bonanno.
Lin Li, Donal O’Regan
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Critical Growth Phases for Adult Shortness [PDF]

American Journal of Epidemiology, 2000
Previous growth studies have not explored how different growth phases-the fetal, infancy, childhood, and puberty phases-interact with each other in the development of adult shortness. In this paper, the authors attempt to describe the importance of each growth phase for adult shortness and the effect of growth in one phase on other, subsequent phases ...
Luo, ZC, Karlberg, J
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Finance and Growth: A Critical Survey* [PDF]

Economic Record, 2006
We present a survey of the finance‐growth nexus that raises a number of qualifications to the standard interpretation. We investigate doubts regarding empirical consensus and we consider the prevalence of cross‐section econometrics as dominant in shaping the present theoretical consensus.
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Critical transitions and perturbation growth directions [PDF]

Physical Review E, 2017
Critical transitions occur in a variety of dynamical systems. Here, we employ quantifiers of chaos to identify changes in the dynamical structure of complex systems preceding critical transitions. As suitable indicator variables for critical transitions, we consider changes in growth rates and directions of covariant Lyapunov vectors. Studying critical
Sharafi, Nahal, Timme, Marc, Hallerberg, Sarah   +2 more
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Existence and multiplicity of standing wave solutions for perturbed fractional p-Laplacian systems involving critical exponents

AIMS Mathematics, 2023
In this paper, we investigate the existence of standing wave solutions to the following perturbed fractional p-Laplacian systems with critical nonlinearity $ \begin{equation*} \left\{ \begin{aligned} &\varepsilon^{ps}(-\Delta)^{s}_{p}u + V(x)|u ...
Shulin Zhang
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