Existence and multiplicity of solutions for semilinear elliptic equations with critical weighted Hardy–Sobolev exponents

Abstract Some existence results are obtained for solutions of semilinear elliptic equations with critical weighted Hardy–Sobolev exponents and superlinear nonlinearity by the variational methods and some analysis techniques.

[1]  Nassif Ghoussoub,et al.  Multiple solutions for quasi-linear PDEs involving the critical Sobolev and Hardy exponents , 2000 .

[2]  Dongsheng Kang,et al.  Positive solutions for singular critical elliptic problems , 2004, Appl. Math. Lett..

[3]  Elliott H. Lieb,et al.  A Relation Between Pointwise Convergence of Functions and Convergence of Functionals , 1983 .

[4]  Susanna Terracini,et al.  On positive entire solutions to a class of equations with a singular coefficient and critical exponent , 1996, Advances in Differential Equations.

[5]  Chun-Lei Tang,et al.  Existence and multiplicity of positive solutions for a class of semilinear elliptic equations involving Hardy term and Hardy–Sobolev critical exponents☆ , 2008 .

[6]  D. Kang On the elliptic problems with critical weighted Sobolev–Hardy exponents , 2007 .

[7]  Nassif Ghoussoub,et al.  Hardy–Sobolev critical elliptic equations with boundary singularities , 2004 .

[8]  Dongsheng Kang,et al.  Solutions for semilinear elliptic problems with critical Sobolev-Hardy exponents and Hardy potential , 2005, Appl. Math. Lett..

[9]  Filippo Gazzola,et al.  Existence of Solutions for Singular Critical Growth Semilinear Elliptic Equations , 2001 .

[10]  W. Rudin Real and complex analysis , 1968 .

[11]  B. Abdellaoui,et al.  Some results for semilinear elliptic equations with critical potential , 2002, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[12]  W. D. Evans,et al.  PARTIAL DIFFERENTIAL EQUATIONS , 1941 .

[13]  Ling Ding,et al.  Existence and multiplicity of solutions for semilinear elliptic equations with Hardy terms and Hardy-Sobolev critical exponents , 2007, Appl. Math. Lett..

[14]  J. García Azorero,et al.  Hardy Inequalities and Some Critical Elliptic and Parabolic Problems , 1998 .

[15]  Remarks on elliptic problems involving the Caffarelli-Kohn-Nirenberg inequalities , 2007 .

[16]  Daomin Cao,et al.  Solutions for semilinear elliptic equations with critical exponents and Hardy potential , 2004 .

[17]  K. Chou,et al.  On the Best Constant for a Weighted Sobolev‐Hardy Inequality , 1993 .

[18]  Florin Catrina,et al.  On the Caffarelli-Kohn-Nirenberg inequalities: Sharp constants, existence (and nonexistence), and symmetry of extremal functions † , 2001 .

[19]  Meilin Lin Some further results for a class of weighted nonlinear elliptic equations , 2008 .

[20]  Robert V. Kohn,et al.  First order interpolation inequalities with weights , 1984 .