Skip to main content
Log in

Semilinear elliptic boundary value problems with small parameters

  • Published:
Archive for Rational Mechanics and Analysis Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Bibliography

  1. Agmon, S., A. Douglis, & L. Nirenberg, Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions, I. Comm. Pure Appl. Math. 12, 623–727 (1959)

    MATH  Google Scholar 

  2. Berger, M. S., & L. E. Fraenkel, On the asymptotic solution of a nonlinear Dirichlet problem. J. Math. Mech. 19, 553–585 (1969/70)

    Google Scholar 

  3. Berger, M. S., & L. E. Fraenkel, On singular perturbations of nonlinear operator equations. Indiana University Math. J. 20, 623–631 (1970/71)

    Google Scholar 

  4. Brisk, N. I., On boundary value problems for the equation ɛy″=f(x, y, y′) for small ɛ. Dokl. Akad. Nauk SSSR 95, 429–432 (1954)

    Google Scholar 

  5. Sobolev, S. L., Applications of Functional Analysis in Mathematical Physics. Amer. Math. Soc. Translations, Vol. 7. Providence, R. I. 1963

  6. Tang, M. M., Asymptotic expansions of some quasilinear elliptic equations with small parameter, (to appear)

  7. Vasileva, A. B., & V. A. Tupchiev, Asymptotic formulas for the solution of a boundary value problem in the case of a second order equation containing a small parameter in the term containing the highest derivative. Dokl. Akad. Nauk SSSR 135, 1035–1037 (1960). (=Soviet Math. Doklady 1, 1333–1335 (1960))

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Communicated by A. Erdélyi

This research was supported by the National Science Foundation Grant GP-30255X.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fife, P.C. Semilinear elliptic boundary value problems with small parameters. Arch. Rational Mech. Anal. 52, 205–232 (1973). https://doi.org/10.1007/BF00247733

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00247733

Keywords

Navigation