References
Adimurthi & G. Mancini, The Neumann problem for elliptic equations with critical non-linearity, preprint.
Adimurthi & S. L. Yadava, Elementary proof of the non-existence of nodal solutions for the semilinear elliptic equations with Critical Sobolev exponent, Nonlin. Anal., T.M.A. 14 (1990), 785–787.
Adimurthi & S. L. Yadava, Critical Sobolev exponent problem in ℝn (n≧ 4) with Neumann boundary condition, Proc. Ind. Acad. of Sci., to appear.
Adimurthi, M. C. Knaap & S. L. Yadava, A note on a critical exponent problem with Neumann boundary conditions, preprint.
F. V. Atkinson & L. A. Peletier, Emden-Fowler equations involving critical exponents, Nonlin. Anal. T.M.A. 10 (1986), 755–776.
F. V. Atkinson, H. Birezis & L. A. Peletier, Solutions qui changent de signe d'equations elliptiques avec exposant de Sobolev critique, C. R. Acad. Sci., Paris 306 (1988), 711–714.
H. Brezis, Nonlinear elliptic equations involving the Critical Sobolev exponent — survey and perspectives, Directions in partial differential equations, edited by M. G. Crandall et al. 1987, 17–36.
H. Brezis & L. Nirenberg, Positive solutions of nonlinear elliptic equations involving critical exponents, Comm. Pure Appl. Math. 36 (1983), 437–477.
C. Budd, M. C. Knaap & L. A. Peletier, Asymptotic behaviour of solutions of elliptic equations with critical exponents and Neumann boundary conditions, preprint.
C. S. Lin & W. M. Ni, On the diffusion coefficient of a semilinear Neumann problem, Springer Lecture Notes 340, 1986.
C. S. Lin, W. M. Ni & I. Takagi, Large amplitude stationary solutions to a chemotaxis system, J. Diff. Eqns. 72 (1988), 1–27.
W. M. Ni, On he positive radial solutions of some semilinear elliptic equations on ℝn, Appl. Math. Optim. 9 (1983), 373–380.
X. J. Wang, Neumann problem of semilinear elliptic equations involving critical Sobolev exponents, J. Diff. Eqns., to appear.
P. Hess & S. Senn, On positive solutions of a linear elliptic eigenvalue problem with Neumann boundary conditions, Math. Annalen 258 (1982), 459–470.
Author information
Authors and Affiliations
Additional information
Communicated by J. Serrin
Rights and permissions
About this article
Cite this article
Adimurthi, Yadava, S.L. Existence and nonexistence of positive radial solutions of neumann problems with critical Sobolev exponents. Arch. Rational Mech. Anal. 115, 275–296 (1991). https://doi.org/10.1007/BF00380771
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00380771