Multiplicity results for a class of asymptotically p-linear equations on ℝN

2016 ◽  
Vol 18 (01) ◽  
pp. 1550031 ◽  
Author(s):  
Rossella Bartolo ◽  
Anna Maria Candela ◽  
Addolorata Salvatore
Keyword(s):  
Elliptic Equation ◽  
Sobolev Spaces ◽  
Weak Solutions ◽  
Quasilinear Elliptic Equation ◽  
Linear Equations ◽  
Weighted Sobolev Spaces ◽  
Embedding Theorem ◽  
Multiplicity Results ◽  
Quasilinear Elliptic

The aim of this paper is investigating the multiplicity of weak solutions of the quasilinear elliptic equation [Formula: see text] in [Formula: see text], where [Formula: see text], the nonlinearity [Formula: see text] behaves as [Formula: see text] at infinity and [Formula: see text] is a potential satisfying suitable assumptions so that an embedding theorem for weighted Sobolev spaces holds. Both the non-resonant and resonant cases are analyzed.

scholarly journals On singular quasilinear elliptic equations with data measures

2021 ◽  
Vol 10 (1) ◽  
pp. 1284-1300
Author(s):  
Nour Eddine Alaa ◽  
Fatima Aqel ◽  
Laila Taourirte
Keyword(s):  
Elliptic Equation ◽  
Weak Solutions ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equation ◽  
Sufficient Conditions ◽  
Existence Results ◽  
Quasilinear Elliptic Equations ◽  
Main Ingredient ◽  
Uniqueness Results ◽  
Quasilinear Elliptic

Abstract The aim of this work is to study a quasilinear elliptic equation with singular nonlinearity and data measure. Existence and non-existence results are obtained under necessary or sufficient conditions on the data, where the main ingredient is the isoperimetric inequality. Finally, uniqueness results for weak solutions are given.

Optimal C1,α estimates for a class of elliptic quasilinear equations

2019 ◽  
Vol 22 (05) ◽  
pp. 1950014 ◽  
Author(s):  
Damião J. Araújo ◽  
Lei Zhang
Keyword(s):  
Elliptic Equation ◽  
Weak Solutions ◽  
Quasilinear Elliptic Equation ◽  
Source Term ◽  
Quasilinear Equations ◽  
Asymptotically Optimal ◽  
Laplacian Equation ◽  
Varying Coefficients ◽  
Quasilinear Elliptic ◽  
Special Case

In this paper, we establish sharp [Formula: see text] estimates for weak solutions of singular and degenerate quasilinear elliptic equation [Formula: see text] which includes the standard [Formula: see text]-Laplacian equation with varying coefficients as a special case. The sharp exponent [Formula: see text] is asymptotically optimal and is determined by the Hölder regularity of the coefficients, the exponent [Formula: see text] and the [Formula: see text]-integrability of the source term [Formula: see text].

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