Results 1 to 10 of about 8,578,478 (315)
Existence of positive radial solutions of general quasilinear elliptic systems [PDF]
Advances in Nonlinear Analysis, 2023 Let Ω⊂Rn(n≥2)\Omega \subset {{\mathbb{R}}}^{n}\hspace{0.33em}\left(n\ge 2) be either an open ball BR{B}_{R} centred at the origin or the whole space. We study the existence of positive, radial solutions of quasilinear elliptic systems of the form Δpu=f1(∣
Devine Daniel
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On Positive Radial Solutions for a Class of Elliptic Equations [PDF]
The Scientific World Journal, 2014 A class of elliptic boundary value problem in an exterior domain is considered under some conditions concerning the first eigenvalue of the relevant linear operator, where the variables of nonlinear term fs,u need not to be separated.
Ying Wu, Guodong Han
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Classification of positive radial solutions to a weighted biharmonic equation [PDF]
Communications on Pure and Applied Analysis, 2021 In this paper, we consider the weighted fourth order equation \begin{document}$ \Delta(|x|^{-\alpha}\Delta u)+\lambda \text{div}(|x|^{-\alpha-2}\nabla u)+\mu|x|^{-\alpha-4}u = |x|^\beta u^p\quad \text{in} \quad \mathbb{R}^n \backslash \{0\}, $\end ...
Yuhao Yan
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Existence of positive radial solutions for a semipositone elliptic equation
Journal of Mathematical Analysis and Applications, 2020 In this paper, we study the existence of positive radial solutions for a semipositone elliptic equation − Δ u = λ f ( u ) in Ω , u = 0 on ∂ Ω , where Ω is a ball or an annulus in R N with N ≥ 2 , λ > 0 is a parameter and f is a continuous function ...
R. Kajikiya, Eunkyung Ko
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Asymptotic behavior of positive radial solutions to elliptic equations approaching critical growth
Electronic Journal of Differential Equations, 2020 We study the asymptotic behavior of radially symmetric solutions to the subcritical semilinear elliptic problem $$\displaylines{ -\Delta u = u^{\frac{N+2}{N-2}}/[\log(e+u)]^{\alpha}\quad \text{in } \Omega=B_R(0)\subset\mathbb{R}^N,\cr u>0,\quad \text{in
Rosa Pardo, Arturo Sanjuan
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Positive radial solutions to classes of nonlinear elliptic systems on the exterior of a ball
Journal of Mathematical Analysis and Applications, 2020 We study positive radial solutions to n × n nonlinear elliptic systems of the form: { − Δ u i = λ K i ( | x | ) f i ( u i + 1 ) in x ∈ Ω E , u i = 0 on | x | = r 0 , u i → 0 as | x | → ∞ , where i ∈ { 1 , 2 , … , n } , u 1 ≡ u n + 1 , Δ u : = div ( ∇ u )
B. Son, Pei-Yong Wang
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Monotonic convergence of positive radial solutions for general quasilinear elliptic systems [PDF]
Nonlinearity, 2023 We study the asymptotic behavior of positive radial solutions for quasilinear elliptic systems that have the form Δpu=c1|x|m1⋅g1v⋅|∇u|αin Rn,Δpv=c2|x|m2⋅g2v⋅g3|∇u|in Rn, where Δp denotes the p-Laplace operator, p > 1, n⩾2 , c1,c2>0 and m1,m2,α⩾0 .
Daniel Devine, Paschalis Karageorgis
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Existence and nonexistence of positive radial solutions of a quasilinear Dirichlet problem with diffusion [PDF]
Journal of Differential Equations, 2022 In this paper existence and nonexistence results of positive radial solutions of a Dirichlet $m$-Laplacian problem with different weights and a diffusion term inside the divergence of the form $\big(a(|x|)+g(u)\big)^{-\gamma}$, with $\gamma>0$ and $a ...
Laura Baldelli +2 more
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Existence of positive global radial solutions to nonlinear elliptic systems
Electronic Journal of Differential Equations, 2023 In this article we obtain global positive and radially symmetric solutions to the system of nonlinear elliptic equations $$ \operatorname{div}\big(\phi_j(|\nabla u|) \nabla u\big) +a_j(x)\phi_j(|\nabla u|) |\nabla u| =p_j(x)f_j(u_1(x),\dots,u_k(x))\,, $$
Seshadev Padhi, Julio G. Dix
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Opuscula Mathematica, 2023 In this paper the authors study the existence of positive radial solutions to the Kirchhoff type problem involving the \(p\)-Laplacian \[-\Big(a+b\int_{\Omega_e}|\nabla u|^p dx\Big)\Delta_p u=\lambda f\left(|x|,u\right),\ x\in \Omega_e,\quad u=0\ \text ...
J. Graef, Doudja Hebboul, T. Moussaoui
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