scholarly journals On some semilinear elliptic equation involving exponential growth

2014 ◽  
Vol 33 ◽  
pp. 23-28 ◽  
Author(s):  
Sami Aouaoui
Keyword(s):  
Elliptic Equation ◽  
Exponential Growth ◽  
Semilinear Elliptic Equation ◽  
Semilinear Elliptic

Positive Solutions for Elliptic Equations With Supercritical Nonlinearity

2009 ◽  
Vol 9 (3) ◽  
Author(s):  
Paulo Rabelo
Keyword(s):  
Elliptic Equation ◽  
Elliptic Equations ◽  
A Priori Estimates ◽  
A Priori ◽  
Auxiliary Problem ◽  
Semilinear Elliptic Equation ◽  
Minimax Methods ◽  
Semilinear Elliptic ◽  
Priori Estimates ◽  
Supercritical Nonlinearity

AbstractIn this paper minimax methods are employed to establish the existence of a bounded positive solution for semilinear elliptic equation of the form−∆u + V (x)u = P(x)|u|where the nonlinearity has supercritical growth and the potential can change sign. The solutions of the problem above are obtained by proving a priori estimates for solutions of a suitable auxiliary problem.

Multi-bump solutions of -Δn = K(x)u (n+2)/(n-2) on lattices in ℝ n

2018 ◽  
Vol 2018 (743) ◽  
pp. 163-211 ◽  
Author(s):  
Yanyan Li ◽  
Juncheng Wei ◽  
Haoyuan Xu
Keyword(s):  
Elliptic Equation ◽  
Critical Exponent ◽  
Critical Point ◽  
Semilinear Elliptic Equation ◽  
Natural Conditions ◽  
Semilinear Elliptic ◽  
Infinite Lattices

Abstract We consider the following semilinear elliptic equation with critical exponent: Δ u = K(x) u^{(n+2)/(n-2)} , u > 0 in \mathbb{R}^{n} , where {n\geq 3} , {K>0} is periodic in ( x_{1} ,…, x_{k} ) with 1 \leq k < (n-2)/2. Under some natural conditions on K near a critical point, we prove the existence of multi-bump solutions where the centers of bumps can be placed in some lattices in {\mathbb{R}^{k}} , including infinite lattices. We also show that for k \geq (n-2)/2, no such solutions exist.

Morse index and symmetry breaking for an elliptic equation with negative exponent in expanding annuli

2017 ◽  
Vol 147 (6) ◽  
pp. 1215-1232
Author(s):  
Zongming Guo ◽  
Linfeng Mei ◽  
Zhitao Zhang
Keyword(s):  
Elliptic Equation ◽  
Symmetry Breaking ◽  
Morse Index ◽  
Blow Up ◽  
Semilinear Elliptic Equation ◽  
Radial Solutions ◽  
Entire Solutions ◽  
Semilinear Elliptic ◽  
Image Position

Bifurcation of non-radial solutions from radial solutions of a semilinear elliptic equation with negative exponent in expanding annuli of ℝ2 is studied. To obtain the main results, we use a blow-up argument via the Morse index of the regular entire solutions of the equationThe main results of this paper can be seen as applications of the results obtained recently for finite Morse index solutions of the equationwith N ⩾ 2 and p > 0.

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