Existence and nonexistence of solutions of nonlinear Neumann problems

SIAM Journal on Mathematical Analysis

Volumn 31, Issue 1, 1999, Pages 119-133

  Pohozaev, Stanislav I ^a   Tesei, Alberto ^b  

^a STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

^b SAPIENZA UNIVERSITY OF ROME   (Italy)

Author keywords

Existence of solutions; Fibering method; Neumann problems; Nonnegative solutions; Problems of indefinite type; Variational methods

Indexed keywords

EID: 0033233502     PISSN: 00361410     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036141098334948     Document Type: Article

References (18)

1. H. AMANN AND M. RENARDY, Reaction-diffusion problems in electrolysis, NoDEA Nonlinear Differential Equations Appl., 1 (1994), pp. 91-117.
2. C. BANDLE, M. A. POZIO, AND A. TESEI, Existence and uniqueness of solutions of nonlinear Neumann problems, Math. Z., 199 (1988), pp. 257-278.
3. H. BERESTYCKI, I. CAPUZZO-DOLCETTA, AND L. NIRENBERG, Variational methods for indefinite superlinear homogeneous elliptic problems, NoDEA Nonlinear Differential Equations Appl., 2 (1995), pp. 553-572.
4. T. F. CHEN, H. A. LEVINE, AND P. E. SACKS, Analysis of a convective reaction-diffusion equation, Nonlinear Anal., 12 (1988), pp. 1349-1370.
5. S. CLAUDI, L. A. PELETIER, AND A. TESEI, A nonlinear diffusion equation involving convection and singular absorption, J. Math. Anal. Appl., 239 (1999).
6. 1+αLocal regularity of weak solutions of degenerate elliptic equations, Nonlinear Anal., 7 (1983), pp. 827-850.
7. P. DRÁBEK, Strongly nonlinear degenerate and singular elliptic problems, in Nonlinear Partial Differential Equations (Fes, 1994), Pitman Res. Notes Math. Ser. 343, Longman, Harlow, UK, 1996, pp. 112-146.
8. P. DRÁBEK AND S. I. POHOZAEV, Positive solutions for the p-Laplacian: Application of the fibering method, Proc. Roy. Soc. Edinburgh Sect. A, 127 (1997), pp. 703-726.
9. P. HESS AND T. KATO, On some linear and nonlinear eigenvalue problems with an indefinite weight function, Comm. Partial Differential Equations, 5 (1980), pp. 999-1030.
10. G. M. LIEBERMAN, Boundary regularity for solutions of degenerate elliptic equations, Nonlinear Anal., 12 (1988), pp. 1203-1219.
11. G. M. LIEBERMAN, Boundary regularity for solutions of degenerate parabolic equations, Nonlinear Anal., 14 (1990), pp. 501-524.
12. T. NAMBA, Density-dependent dispersal and spatial distribution of a population, J. Theoret. Biol., 86 (1980), pp. 351-363.
13. S. I. POHOZAEV, On an approach to nonlinear equations, Soviet Math. Dokl., 20 (1979), pp. 912-916. Translation of Dokl. Akad. Nauk. SSSR, 247 (1979), pp. 1327-1331.
14. S. I. POHOZAEV, On an approach to nonlinear equations, Soviet Math. Dokl., 20 (1979), pp. 912-916. Translation of Dokl. Akad. Nauk. SSSR, 247 (1979), pp. 1327-1331.
15. S. I. POHOZAEV, On a constructive method in the calculus of variations, Soviet Math. Dokl., 37 (1988), pp. 274-277. Translation of Dokl. Akad. Nauk. SSSR, 298 (1988), pp. 1330-1333.
16. S. I. POHOZAEV, On a constructive method in the calculus of variations, Soviet Math. Dokl., 37 (1988), pp. 274-277. Translation of Dokl. Akad. Nauk. SSSR, 298 (1988), pp. 1330-1333.
17. S. I. POHOZAEV, On the method of fibering a solution in nonlinear boundary value problems, Proc. Steklov Inst. Math., 3 (1992), pp. 157-173.
18. P. TOLKSDORF, Regularity for a more general class of quasilinear elliptic equations, J. Differential Equations, 51 (1984), pp. 126-150.