scholarly journals Infinitely many sign-changing solutions for a semilinear elliptic equation with variable exponent

2021 ◽  
Vol 6 (6) ◽  
pp. 5720-5736
Author(s):  
Changmu Chu ◽  
◽  
Yuxia Xiao ◽  
Yanling Xie
Keyword(s):  
Elliptic Equation ◽  
Variable Exponent ◽  
Semilinear Elliptic Equation ◽  
Semilinear Elliptic ◽  
Sign Changing Solutions

A Singular Semilinear Elliptic Equation with a Variable Exponent

2016 ◽  
Vol 16 (3) ◽  
Author(s):  
José Carmona ◽  
Pedro J. Martínez-Aparicio
Keyword(s):  
Elliptic Equation ◽  
Elliptic Equations ◽  
Variable Exponent ◽  
Model Problem ◽  
Semilinear Elliptic Equation ◽  
Semilinear Elliptic Equations ◽  
Bounded Set ◽  
Semilinear Elliptic

AbstractIn this paper we consider singular semilinear elliptic equations with a variable exponent whose model problem isHere Ω is an open bounded set of

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.

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