Radially Symmetric Solutions for Quasilinear Elliptic Equations Involving Nonhomogeneous Operators in an Orlicz-Sobolev Space Setting

2020 ◽  
Vol 40 (6) ◽  
pp. 1679-1699
Author(s):  
Jae-Myoung Kim ◽  
Yun-Ho Kim ◽  
Jongrak Lee
Keyword(s):  
Sobolev Space ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Space Setting ◽  
Radially Symmetric Solutions ◽  
Quasilinear Elliptic

scholarly journals Multiplicity of Radially Symmetric Small Energy Solutions for Quasilinear Elliptic Equations Involving Nonhomogeneous Operators

Mathematics ◽  
2020 ◽  
Vol 8 (1) ◽  
pp. 128
Author(s):  
Jun Ik Lee ◽  
Yun-Ho Kim
Keyword(s):  
Elliptic Equations ◽  
Quasilinear Elliptic Equation ◽  
Functional Method ◽  
Quasilinear Elliptic Equations ◽  
Fountain Theorem ◽  
Small Energy ◽  
Dual Fountain Theorem ◽  
Radially Symmetric Solutions ◽  
Quasilinear Elliptic ◽  
Modified Functional

We investigate the multiplicity of radially symmetric solutions for the quasilinear elliptic equation of Kirchhoff type. This paper is devoted to the study of the L ∞ -bound of solutions to the problem above by applying De Giorgi’s iteration method and the localization method. Employing this, we provide the existence of multiple small energy radially symmetric solutions whose L ∞ -norms converge to zero. We utilize the modified functional method and the dual fountain theorem as the main tools.

scholarly journals Oblique derivative problem for quasilinear elliptic equations with VMO coefficients

1996 ◽  
Vol 53 (3) ◽  
pp. 501-513 ◽  
Author(s):  
Guiseppe Di Fazio ◽  
Dian K. Palagachev
Keyword(s):  
Sobolev Space ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equations ◽  
Oblique Derivative Problem ◽  
Strong Solvability ◽  
Derivative Problem ◽  
Carathéodory Functions ◽  
Vmo Coefficients ◽  
Image Position ◽  
Quasilinear Elliptic

Strong solvability and uniqueness in the Sobolev space W2, q(Ω), q > n, are proved for the oblique derivative problemassuming the coefficients of the quasilinear elliptic operator to be Carathéodory functions, aij ∈ VMO∩L∞ with respect to x, and b to grow at most quadratically with respect to the gradient.

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