Elliptic equations of order in annular domains

Author:
Robert Dalmasso

Journal:
Trans. Amer. Math. Soc. **347** (1995), 3575-3585

MSC:
Primary 35B05; Secondary 34B15, 35J65

DOI:
https://doi.org/10.1090/S0002-9947-1995-1311907-8

MathSciNet review:
1311907

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we study the existence of positive radial solutions for some semilinear elliptic problems of order in an annulus with Dirichlet boundary conditions. We consider a nonlinearity which is either sublinear or the sum of a sublinear and a superlinear term.

**[1]**A. Ambrosetti, H. Brezis and G. Cerami,*Combined effects of concave and convex nonlinearities in some elliptic problems*, J. Funct. Anal.**122**(1994), 519-543. MR**1276168 (95g:35059)****[2]**D. Arcoya,*Positive solutions for semilinear Dirichlet problems in an annulus*, J. Differential Equations**94**(1991), 217-227. MR**1137613 (92j:35058)****[3]**C. Bandle and M. Kwong,*Semilinear elliptic problems in annular domains*, J. Appl. Math. Phys.**40**(1989), 245-257. MR**990630 (90m:35062)****[4]**C. Bandle, C. V. Coffman and M. Marcus,*Nonlinear elliptic problems in annular domains*, J. Differential Equations**69**(1987), 322-345. MR**903391 (89a:35082)****[5]**P. W. Bates and G. B. Gustafson,*Green's function inequalities for two-point boundary value problems*, Pacific J. Math.**59**(1975), 327-343. MR**0437841 (55:10762)****[6]**C. V. Coffman and M. Marcus,*Existence and uniqueness results for semilinear Dirichlet problems in annuli*, Arch. Rational Mech. Anal.**108**(1989), 293-307. MR**1013459 (90m:35064)****[7]**W. A. Coppel,*Disconjugacy*, Lectures Notes in Math., vol. 220, Springer-Verlag, New York, 1971. MR**0460785 (57:778)****[8]**R. Dalmasso,*Positive radial solutions for semilinear biharmonic equations in annular domains*, Rev. Mat. Universidad Complut. Madrid**6**(1993), 279-294. MR**1269758 (95a:35044)****[9]**-,*Positive radial solutions of semilinear equations of order**in annular domains*, Hokkaido Math. J.**23**(1994), 93-103. MR**1263825 (94m:35019)****[10]**D. De Figueiredo, P. L. Lions and R. D. Nussbaum,*A priori estimates and existence of positive solutions of semilinear elliptic equations*, J. Math. Pures Appl.**61**(1982), 41-63. MR**664341 (83h:35039)****[11]**X. Garaizar,*Existence of positive radial solutions for semilinear elliptic equations in the annulus*, J. Differential Equations**70**(1987), 69-92. MR**904816 (89f:35019)****[12]**M. A. Krasnosel'skii,*Positive solutions of operator equations*, Noordhoff, Groningen, 1964. MR**0181881 (31:6107)****[13]**S. S. Lin,*On the existence of positive radial solutions for nonlinear elliptic equations in annular domains*, J. Differential Equations**81**(1989), 221-233. MR**1016080 (90i:35023)****[14]**M. A. Naimark,*Elementary theory of linear differential operators*, Part I, Ungar, New York, 1967.**[15]**H. Wang,*On the existence of positive solutions for semilinear elliptic equations in the annulus*, J. Differential Equations**109**(1994), 1-7. MR**1272398 (95c:35093)**

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1995-1311907-8

Keywords:
Semilinear elliptic equations,
Green's function,
fixed point theorems

Article copyright:
© Copyright 1995
American Mathematical Society