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Semilinear elliptic boundary value problems with small parameters. (English) Zbl 0268.35007

MSC:
35J25 Boundary value problems for second-order elliptic equations
35B20 Perturbations in context of PDEs
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[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) · Zbl 0093.10401 · doi:10.1002/cpa.3160120405
[2] Berger, M. S., & L. E. Fraenkel, On the asymptotic solution of a nonlinear Dirichlet problem. J. Math. Mech. 19, 553–585 (1969/70) · Zbl 0203.10402
[3] Berger, M. S., & L. E. Fraenkel, On singular perturbations of nonlinear operator equations. Indiana University Math. J. 20, 623–631 (1970/71) · Zbl 0218.47031 · doi:10.1512/iumj.1971.20.20050
[4] Brisk, N. I., On boundary value problems for the equation y”=f(x, y, y’) for small . Dokl. Akad. Nauk SSSR 95, 429–432 (1954)
[5] Sobolev, S. L., Applications of Functional Analysis in Mathematical Physics. Amer. Math. Soc. Translations, Vol. 7. Providence, R. I. 1963 · Zbl 0123.09003
[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))
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