scholarly journals Nonexistence of solutions for elliptic equations with supercritical nonlinearity in nearly nontrivial domains

2020 ◽  
Vol 31 (1) ◽  
pp. 121-130
Author(s):  
Riccardo Molle ◽  
Donato Passaseo
Keyword(s):  
Elliptic Equations ◽  
Nonexistence Of Solutions ◽  
Supercritical Nonlinearity

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.

QUASILINEAR ELLIPTIC EQUATIONS WITH SINGULAR QUADRATIC GROWTH TERMS

2011 ◽  
Vol 13 (04) ◽  
pp. 607-642 ◽  
Author(s):  
LUCIO BOCCARDO ◽  
TOMMASO LEONORI ◽  
LUIGI ORSINA ◽  
FRANCESCO PETITTA
Keyword(s):  
Positive Solutions ◽  
Lebesgue Space ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Quadratic Growth ◽  
Open Set ◽  
Existence And Nonexistence ◽  
Nonexistence Of Solutions ◽  
Quasilinear Problems ◽  
Quasilinear Elliptic

In this paper, we deal with positive solutions for singular quasilinear problems whose model is [Formula: see text] where Ω is a bounded open set of ℝN, g ≥ 0 is a function in some Lebesgue space, and γ > 0. We prove both existence and nonexistence of solutions depending on the value of γ and on the size of g.

Liouville-type theorems for elliptic equations in half-space with mixed boundary value conditions

2016 ◽  
Vol 8 (1) ◽  
pp. 193-202 ◽  
Author(s):  
Abdellaziz Harrabi ◽  
Belgacem Rahal
Keyword(s):  
Elliptic Equations ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Nonlinear Elliptic Equations ◽  
Monotonicity Formula ◽  
Compact Set ◽  
Liouville Type ◽  
Nonlinear Elliptic ◽  
Liouville Type Theorems ◽  
Nonexistence Of Solutions

Abstract In this paper we study the nonexistence of solutions, which are stable or stable outside a compact set, possibly unbounded and sign-changing, of some nonlinear elliptic equations with mixed boundary value conditions. The main methods used are the integral estimates and the monotonicity formula.

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