An existence result for a fractional elliptic system involving (p,q)-Laplacian and critical exponent

2022 ◽  
pp. 1-17
Author(s):  
Aini Zhang ◽  
Zhiying Deng
Keyword(s):  
Critical Exponent ◽  
Elliptic System ◽  
Existence Result

scholarly journals Existence of Nontrivial Solutions for Perturbed Elliptic System inℝN

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Juan Jiang
Keyword(s):  
Variational Method ◽  
Critical Exponent ◽  
Elliptic System ◽  
Existence Result ◽  
Nonlinear Elliptic System ◽  
Nontrivial Solutions ◽  
Nonlinear Elliptic ◽  
Sobolev Critical Exponent

We consider the perturbed nonlinear elliptic system-ε2Δu+V(x)u=K(x)|u|2*-2u+Hu(u,v),  x∈ℝN,-ε2Δv+V(x)v=K(x)|v|2*-2v+Hv(u,v),  x∈ℝN, whereN≥3,2*=2N/(N-2)is the Sobolev critical exponent. Under proper conditions onV,H, andK, the existence result and multiplicity of the system are obtained by using variational method providedεis small enough.

scholarly journals An elliptic problem with critical exponent and positive Hardy potential

2004 ◽  
Vol 2004 (2) ◽  
pp. 91-98
Author(s):  
Shaowei Chen ◽  
Shujie Li
Keyword(s):  
Critical Exponent ◽  
Elliptic Problem ◽  
Existence Result ◽  
Hardy Potential

We give the existence result and the vanishing order of the solution in0for the following equation:−Δu(x)+(μ/|x|2)u(x)=λu(x)+u2*−1(x), wherex∈B1,μ>0, and the potentialμ/|x|2−λis positive inB1.

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