scholarly journals Existence and nonexistence of entire positive radial solutions for a class of Schrödinger elliptic systems involving a nonlinear operator

2018 ◽  
Vol 0 (0) ◽  
pp. 0-0
Author(s):  
Zedong Yang ◽  
◽  
Guotao Wang ◽  
Ravi P. Agarwal ◽  
Haiyong Xu ◽  
...  
Keyword(s):  
Nonlinear Operator ◽  
Elliptic Systems ◽  
Radial Solutions ◽  
Positive Radial Solutions ◽  
Existence And Nonexistence

scholarly journals Non-existence of ground states for a semilinear elliptic system of Lane-Emden-Fowler type

2013 ◽  
Vol 29 (2) ◽  
pp. 187-193
Author(s):  
MIODRAG IOVANOV ◽  
Keyword(s):  
Elliptic System ◽  
Nonlinear Term ◽  
Sufficient Conditions ◽  
Elliptic Systems ◽  
Aequationes Math ◽  
Radial Solutions ◽  
Semilinear Elliptic ◽  
Semilinear Elliptic System ◽  
Positive Radial Solutions ◽  
Radially Symmetric Solutions

We obtain sufficient conditions for the non-existence of positive radially symmetric solutions for a class of Lane, Emden and Fowler elliptic systems. In our result, the nonlinear term it was suggested by the work of [D. O’Regan and H. Wang, Positive radial solutions for p-Laplacian systems, Aequationes Math., 75 (2008) 43–50].

Coercive elliptic systems with gradient terms

2017 ◽  
Vol 6 (2) ◽  
pp. 165-182 ◽  
Author(s):  
Roberta Filippucci ◽  
Federico Vinti
Keyword(s):  
Blow Up ◽  
Elliptic Systems ◽  
Continuous Functions ◽  
Necessary Condition ◽  
Bounded Solutions ◽  
Radial Solutions ◽  
Existence Of A Solution ◽  
Content Type ◽  
Positive Radial Solutions

AbstractIn this paper we give a classification of positive radial solutions of the following system:$\Delta u=v^{m},\quad\Delta v=h(|x|)g(u)f(|\nabla u|),$in the open ball ${B_{R}}$, with ${m>0}$, and f, g, h nonnegative nondecreasing continuous functions. In particular, we deal with both explosive and bounded solutions. Our results involve, as in [27], a generalization of the well-known Keller–Osserman condition, namely, ${\int_{1}^{\infty}(\int_{0}^{s}F(t)\,dt)^{-m/(2m+1)}\,ds<\infty}$, where ${F(t)=\int_{0}^{t}f(s)\,ds}$. Moreover, in the second part of the paper, the p-Laplacian version, given by ${\Delta_{p}u=v^{m}}$, ${\Delta_{p}v=f(|\nabla u|)}$, is treated. When ${p\geq 2}$, we prove a necessary condition for the existence of a solution with at least a blow up component at the boundary, precisely ${\int_{1}^{\infty}(\int_{0}^{s}F(t)\,dt)^{-m/(mp+p-1)}s^{(p-2)(p-1)/(mp+p-1)}% \,ds<\infty}$.

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