On the number of positive solutions for quasilinear elliptic eigenvalue problems

Nonlinear Analysis, Theory, Methods and Applications

Volumn 27, Issue 2, 1996, Pages 229-247

  Guo, Zongming ^a  

^a HENAN NORMAL UNIVERSITY   (China)

Author keywords

Large solutions; Mountain pass lemma; Quasilinear eigenvalues problems; Uniqueness

Indexed keywords

CALCULATIONS; GREEN'S FUNCTION; LINEARIZATION; MATHEMATICAL TRANSFORMATIONS; NONLINEAR EQUATIONS; OPTIMIZATION;

ASYMPTOTIC ESTIMATE; CRITICAL POINT THEORY; EMBEDDING THEOREM; MOUNTAIN PASS LEMMA; POSITIVE SOLUTIONS; QUASILINEAR ELLIPTIC EIGENVALUE PROBLEMS; SOBOLEV INEQUALITY;

EIGENVALUES AND EIGENFUNCTIONS;

EID: 0030193703     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/0362-546X(94)00352-I     Document Type: Article

References (18)

1. GUO Z. M., Some existence and multiplicity results for a class of quasilinear elliptic eigenvalue problems, Nonlinear Analysis 18, 957-971 (1992).
2. GUO Z. M., Existence and uniqueness of positive radial solutins for a class of quasilinear elliptic equations, App. Analysis 47, 173-190 (1992).
3. GUO Z. M. & WEBB J. R. L., Uniqueness of positive solutions for quasilinear elliptic equations when a parameter is large, Proc. R. Soc. Edinb. 124A, 189-198 (1994).
4. ANGENENT S. B., Uniqueness of the solution of a semilinear boundary value problem. Math. Annln 272, 129-138 (1985).
5. BOCCARDO L., ESCOBEDO M. & PERAL I., A Dirichlet problem involving critical exponent, Nonlinear Analysis, 24, 1639-1648 (1995).
6. GUEDDA M. & VERON L., Local and global properties of solutions of quasilinear elliptic equations, J. diff. Eqns 76, 159-189 (1988).
7. KICHENASSARY S. & SMOLLER J., On the existence of radial solutions of quasilinear elliptic equations, Nonlinearity 3, 677-694 (1990).
8. LADYZHENSKAYA O. A. & URAL'TSEVA N. N., Linear and Quasilinear Elliptic Equations. Academic Press, New York (1968).
9. SAKAGUCHI S., Concavity properties of solutions to some degenerate quasilinear elliptic Dirichlet problems, Ann. Scuola Norm. Sup. Pisa. Cl. Sci. (IV) 14, 403-421 (1987).
10. DANCER E. N., Uniqueness for elliptic equations when a parameter is large, Nonlinear Analysis 8, 835-836 (1984).
11. DANCER E. N., On the number of positive solutions of weakly nonlinear elliptic equations when a parameter is large, Proc. London math. Soc. 53(3), 429-452 (1986).
12. LIN S. S., On the number of positive solutions for nonlinear elliptic equations when a parameter is large, Nonlinear Analysis 16, 283-297 (1991).
13. TOLKSDORF P., On the Dirichlet problem for quasilinear equations in domains with conical points, Communs partial diff. Eqns 8(7), 773-817 (1983).
14. SATTINGER D. H., Monotone methods in nonlinear elliptic and parabolic boundary value problems, Indiana Univ. math. J. 21, 979-1000 (1972).
15. GILBARG D. & TRUDINGER N. S., Elliptic Partial Differential Equations of Second Order. Springer-Verlag, Berlin (1977).
16. BERGER M. S., Nonlinearity and Functional Analysis. Academic Press, New York, London (1977).
17. RABINOWITZ P. H., Minimax methods in critical point theory with applications to differential equations, CBMS Regional Conference Series in Mathematics, 65, American Mathematical Society, Providence, Rhode Island (1986).
18. AZORERO J. G., ALONSO I. P. & PUEL J. P., Quasilinear problems with exponential growth in the reaction term, Communs partial diff. Eqns (1995) (to appear).