Existence of nontrivial solution for a quasilinear elliptic equation with (p, q)-Laplacian in $${\mathbb {R}}^N$$ involving critical Sobolev exponents

2020 ◽  
Vol 6 (2) ◽  
pp. 733-749
Author(s):  
M. Latifi ◽  
R. Bayat
Keyword(s):  
Elliptic Equation ◽  
Nontrivial Solution ◽  
Quasilinear Elliptic Equation ◽  
Critical Sobolev Exponents ◽  
Quasilinear Elliptic

scholarly journals Eigenvalue problems for a quasilinear elliptic equation onℝN

2005 ◽  
Vol 2005 (18) ◽  
pp. 2871-2882 ◽  
Author(s):  
Marilena N. Poulou ◽  
Nikolaos M. Stavrakakis
Keyword(s):  
Elliptic Equation ◽  
Weight Function ◽  
Quasilinear Elliptic Equation ◽  
Eigenvalue Problems ◽  
Principal Eigenvalue ◽  
Laplacian Operator ◽  
Quasilinear Elliptic

We prove the existence of a simple, isolated, positive principal eigenvalue for the quasilinear elliptic equation−Δpu=λg(x)|u|p−2u,x∈ℝN,lim|x|→+∞u(x)=0, whereΔpu=div(|∇u|p−2∇u)is thep-Laplacian operator and the weight functiong(x), being bounded, changes sign and is negative and away from zero at infinity.

Existence of Radial Solutions for Quasilinear Elliptic Equations with Singular Nonlinearities

2003 ◽  
Vol 3 (4) ◽  
Author(s):  
Beatrice Acciaio ◽  
Patrizia Pucci
Keyword(s):  
Elliptic Equation ◽  
Elliptic Equations ◽  
Quasilinear Elliptic Equation ◽  
Quasilinear Elliptic Equations ◽  
Radial Solutions ◽  
Singular Nonlinearities ◽  
Quasilinear Elliptic

AbstractWe prove the existence of radial solutions of the quasilinear elliptic equation div(A(|Du|)Du) + f(u) = 0 in ℝ

scholarly journals Norm Comparison Estimates for the Composite Operator

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Xuexin Li ◽  
Yong Wang ◽  
Yuming Xing
Keyword(s):  
Elliptic Equation ◽  
Quasilinear Elliptic Equation ◽  
Differential Forms ◽  
Generalized Solution ◽  
Composite Operator ◽  
Potential Operator ◽  
Norm Estimates ◽  
Quasilinear Elliptic ◽  
Littlewood Maximal Operator ◽  
Norm Comparison

This paper obtains the Lipschitz and BMO norm estimates for the composite operator𝕄s∘Papplied to differential forms. Here,𝕄sis the Hardy-Littlewood maximal operator, andPis the potential operator. As applications, we obtain the norm estimates for the Jacobian subdeterminant and the generalized solution of the quasilinear elliptic equation.

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