This is a preview of subscription content, log in via an institution to check access.
References
C. Bandle, Existence theorems, qualitative results and a priori bounds for a class of nonlinear Dirichlet problems, Arch. Rational Mech. Anal., 58 (1975) 219–238.
J. Bebernes & A. Ederly, Mathematical problems from combustion theory, Springer-Verlag (1989).
H. Brezis & F. Merle, Uniform estimates and blow-up behavior for solutions of -Δu=V(x)eu in two dimensions, preprint.
H. Berestycki & L. Nirenberg, Monotonocity, symmetry and antisymmetry of solutions of semilinear elliptic equations, to appear.
H. Berestycki & L. Nirenberg, Some qualitative properties of solutions of semilinear elliptic equations in cylindrical domains, to appear.
H. Brezis & R. E. L. Turner, On a class of superlinear elliptic problems, Comm. in Partial Diff Eqs., 2 (1977) 601–614.
S. Chandrasekhar, An introduction to the study of stellar structure, New York, Dover (1957).
W. Chen & C. Li, Classification of solutions of some nonlinear elliptic equations, Duke Math. J., 63 (1991) 615–622.
W. Chen & C. Li, Asymptotic behavior of solutions to some nonlinear elliptic equations in R2, preprint.
M. Crandall & P. Rabinowitz, Some continuation and variational methods for positive solutions of nonlinear elliptic eigenvalue problems, Arch. Rational Mech. Anal., 58 (1975) 207–218.
A. Callegari, E. Reiss & H. Keller, Membrane buckling, Comm. Pure Appl. Math., 24 (1971) 499–527.
D. G. de Figueiredo, P.-L. Lions & R. D. Nussbaum, A priori estimates and existence of positive solutions of semilinear elliptic equations, J. Math. Pure et Appl., 61 (1982) 41–63.
I. M. Gelfand, Some problems in the theory of quasilinear equations, Amer. Math. Soc. Transl., 29 (1963) 295–381.
B. Gidas, W. M. Ni & L. Nirenberg, Symmetry and related properties via the maximum principle, Comm. Math. Phys., 68 (1979) 209–243.
B. Gidas, W. M. Ni & L. Nirenberg, Symmetry of positive solutions of nonlinear elliptic equations in Rn, Math. Anal. Appl., Part A, Advances in Math. Suppl. Studies 7A (ed., L. Nachbin), Academic Press (1981) 369–402.
D. Joseph & T. Lundgren, Quasilinear Dirichlet problem driven by positive sources, Arch. Rational Mech. Anal., 49 (1972) 241–269.
D. D. Joseph, Nonlinear heat generation and the stability of the temperature distribution in conducting solids, Int. J. Heat Mass Transfer, 8 (1965) 281–288.
D. D. Joseph & E. M. Sparrow, Nonlinear diffusion induced by nonlinear souces, Quart. Appl. Math., 28 (1970) 327–342.
J. Kazdan, Prescribing the curvature of a Riemannian manifold, C.B.M.S. Lecture 57, Amer. Math. Soc. (1984).
H. Keller & D. Cohen, Some positione problems suggested by nonlinear heat generation, J. Math. Mech., 16 (1967) 1361–1376.
J. Kazdan & F. Warner, Remarks on some quasilinear elliptic equations, Comm. Pure Appl. Math., 38 (1975) 567–597.
C. Li, Monotonicity and symmetry of solutions of fully nonlinear elliptic equations on bounded domains, Comm. Partial Diff. Eqs., 16 (1991) 491–526.
K. Nagasaki & T. Suzuki, On a nonlinear eigenvalue problem, Recent Topics in Nonlinear PDE III, Tokyo, 1986, Lecture Notes in Num. Appl. Anal., 9, North Holland (1987) 185–218.
R. D. Nussbaum, Positive solutions of nonlinear elliptic boundary value problems, J. Math. Anal. Appl., 51 (1975) 461–482.
R. E. L. Turner, A priori bounds for positive solutions of nonlinear elliptic equations in two variables, Duke Math. J., 41 (1974) 759–774.
Author information
Authors and Affiliations
Additional information
Communicated by P. H. Rabinowitz
Rights and permissions
About this article
Cite this article
Chen, W., Li, C. A priori estimates for solutions to nonlinear elliptic equations. Arch. Rational Mech. Anal. 122, 145–157 (1993). https://doi.org/10.1007/BF00378165
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00378165