Entire nodal solutions of a semilinear elliptic equation and their effect on concentration phenomena

2016 ◽  
Vol 437 (1) ◽  
pp. 485-497 ◽  
Author(s):  
Mónica Clapp ◽  
P.N. Srikanth
Keyword(s):  
Elliptic Equation ◽  
Semilinear Elliptic Equation ◽  
Nodal Solutions ◽  
Concentration Phenomena ◽  
Semilinear Elliptic

Existence of 2–Nodal Solutions for Semilinear Elliptic Equations in Unbounded Domains

2010 ◽  
Vol 10 (1) ◽  
pp. 1-21 ◽  
Author(s):  
Tiexiang Li ◽  
Huei-li Lin ◽  
Tsung-fang Wu
Keyword(s):  
Elliptic Equation ◽  
Elliptic Equations ◽  
Unbounded Domains ◽  
Semilinear Elliptic Equation ◽  
Semilinear Elliptic Equations ◽  
Nodal Solutions ◽  
Domain Shape ◽  
Semilinear Elliptic

AbstractIn this paper, we study the effect of domain shape on the existence of 2-nodal solutions for a semilinear elliptic equation involving non-odd nonlinearities.

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.

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