Existence of Solutions for Elliptic Equation with Critical Sobolev Exponent

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In this paper, we consider a class of elliptic equation on unbounded domain. By the variational method, we prove the existence of solutions.

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1205-1208

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February 2013

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© 2013 Trans Tech Publications Ltd. All Rights Reserved

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[1] R.B. Assuncao, P.C. Carriao, O.H. Miyagaki, Critical singular problem via concentration- compactness lemma, J. Math. Anal. Appl. 326 (2007) 137-154.

Google Scholar

[2] M.L. Miotto, O.H. Miyagaki, Multiple positive solutions fro semilinear Dirichlet problems with sign-changing weight function in infinite strip domains, Nonlinear Anal. 71 (2009) 3434-3447.

DOI: 10.1016/j.na.2009.02.010

Google Scholar

[3] Rodrigo da Silva Rodrigues, On elliptic problems involving Hardy-Sobolev exponents and sign-changing function, Nonlinear Anal. 73 (2010) 857-880.

DOI: 10.1016/j.na.2010.03.053

Google Scholar

[4] M.L. Miotto, O.H. Miyagaki, Multiple positive solutions fro semilinear Dirichlet problems with sign-changing weight function in infinite strip domains, Nonlinear Anal. 71 (2009) 3434-3447.

DOI: 10.1016/j.na.2009.02.010

Google Scholar

[5] J.V. Goncalves, C.O. Alves, Existence of positive solutions for m-laplacian equations in involving critical Sobolev exponents, Nonlinear Anal. 32 (1998) 53-70.

DOI: 10.1016/s0362-546x(97)00452-5

Google Scholar

[6] T.F. Wu, On semilinear elliptic equations involving concave-convex nonlinearities and sign-changing weight function, J. Math. Anal. Appl. 318 (2006) 253-270.

DOI: 10.1016/j.jmaa.2005.05.057

Google Scholar

[7] T.F. Wu, On semilinear elliptic equations involving critical Sobolev exponent and sing-changing weight function, Comm. Pure Appl. Anal. 7 (2008) 384-405.

DOI: 10.3934/cpaa.2008.7.383

Google Scholar

[8] G.A. Afrouzi, S.H. Rasouli. A variational approach to a quasilinear elliptic problem involving the p-Laplacian and nonlinear boundary condition. Nonlinear Anal. 71 (2009) 2447-2455.

DOI: 10.1016/j.na.2009.01.090

Google Scholar

[9] J. Garcia-Azorero, I. Peral, J.D. Rossi, A convex-concave problemwith a nonlinear boundary condition, J. Differential Equations 198 (2004) 91-128.

DOI: 10.1016/s0022-0396(03)00068-8

Google Scholar

[10] N. Mavinga, M.N. Nkashama, Steklov-Neumann eigenproblems and nonlinear elliptic equations with nonlinear boundary conditions, J. Differential Equations 248 (2010) 1212-1229.

DOI: 10.1016/j.jde.2009.10.005

Google Scholar

[11] P.L. Lions, The concentration-compactness principle in the calculus of variations, the locally compact case, Ann. Inst. H. Poincare Anal. Nonlineaire 1 (part 1) (1984), pp.109-145; (part 2) (1984), pp.223-283.

DOI: 10.1016/s0294-1449(16)30422-x

Google Scholar

[12] P.L. Lions, The concentration-compactness principle in the calculus of variations, the limit case, Rev. Mat. Ibero Americana 1 (part 1) (1985), pp.145-201; 2 (part 2) (1985), pp.45-121.

DOI: 10.4171/rmi/6

Google Scholar