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On the Growth of Positive Entire Solutions of Elliptic PDEs and Their Gradients
Discrete and Continuous Dynamical Systems - Series S, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Antonio Vitolo
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Nonexistence of Positive Solutions of PDE's with p-Laplacian
Acta Mathematica Hungarica, 2001The authors study the problem of nonexistence of positive solutions of the equation \[ \text{div}\big(||\nabla u||^{p-2}\nabla u\big)+c(x)|u|^{p-2}u=0,\quad x\in \mathbb R^n,\; p>1, \tag{1} \] where \(C: \mathbb R^n\to \mathbb R\) is a Hölder continuous function.
Došlý, O., Mařík, R.
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Communications on Pure and Applied Mathematics, 1994
AbstractWe study the partial differential equation magnified image which arose originally as a scaling limit in the study of interface fluctuations in a certain spin system. In that application x lies in R, but here we study primarily the periodic case × R S1.
Bleher, Pavel M. +2 more
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AbstractWe study the partial differential equation magnified image which arose originally as a scaling limit in the study of interface fluctuations in a certain spin system. In that application x lies in R, but here we study primarily the periodic case × R S1.
Bleher, Pavel M. +2 more
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Fractional Calculus and Applied Analysis, 2020
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Daoues, Adel +2 more
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zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Daoues, Adel +2 more
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Qualitative properties of positive solutions to nonlinear pde and FBP
Nonlinear Analysis: Theory, Methods & Applications, 1996The general goal of the paper is to study the qualitative properties of positive solutions of nonlinear divergence form elliptic equations \[ \nabla\cdot A(x,u,Du)+B(x,u,Du)=0,\quad x\in \Omega\subset\mathbb{R}^N,\quad N\geq 2. \] Applying the moving plane procedure of Aleksandrov, the author establishes star-shapedness of the level sets in certain ...
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Classification of positive smooth solutions to third-order PDEs involving fractional Laplacians
Pacific Journal of Mathematics, 2018This authors study a third-order conformal invariant equation with critical nonlinearity and a third-order critical static Hartree equation with nonlocal nonlinearity. By showing the equivalence between PDE and a integral equation, using some results in [\textit{W. Chen} et al., Commun. Pure Appl. Math. 59, No.
Dai, Wei, Qin, Guolin
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Complex Variables and Elliptic Equations, 2013
In this paper, we consider the following weighted PDE system with Navier boundary conditions on a half space:1 When is any even number between and , we establish the equivalence between (1) and the following integral system2 under some very mild growth condition, where is the reflection of the point about the plane .
Dongyan Li, Pengcheng Niu, Ran Zhuo
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In this paper, we consider the following weighted PDE system with Navier boundary conditions on a half space:1 When is any even number between and , we establish the equivalence between (1) and the following integral system2 under some very mild growth condition, where is the reflection of the point about the plane .
Dongyan Li, Pengcheng Niu, Ran Zhuo
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Structure of positive radial solution to a semilinear elliptic PDE with a gradient-term
Funkcialaj Ekvacioj, 1996Let \(\lambda\in \{0,1\}\), \(n\geq 3\), \(u:[0,+\infty[ \times ]0,+\infty[\to \overline{\mathbb{R}}\), \(u(.,\alpha)\in C^2([0,+\infty[)\), \(\partial^2_1 u(r,\alpha)+ ({{n-1}\over r}+{r\over 2})\partial_i u(r,\alpha)+\lambda u(r,\alpha)+|u(r,\alpha) |^{p-1}u(r,\alpha)= 0\), \(u(0,\alpha)= \alpha\), \(\partial_1u(0,\alpha)= 0\). Then \(u(r,\alpha)>0\)
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2013
We consider a system of nonlinear PDEs describing the reaction-diffusion dynamics near a triple-phase boundary in the catalyst layer of hydrogen fuel cells. The system involves bulk diffusion and surface reaction-diffusion processes and is an approximation of a model with a thin layer.
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We consider a system of nonlinear PDEs describing the reaction-diffusion dynamics near a triple-phase boundary in the catalyst layer of hydrogen fuel cells. The system involves bulk diffusion and surface reaction-diffusion processes and is an approximation of a model with a thin layer.
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