On nonlocal existence results for elliptic equations with convex-concave nonlinearities

Nonlinear Analysis, Theory, Methods and Applications

Volumn 61, Issue 1-2, 2005, Pages 211-236

  Il'yasov, Yavdat ^a  

^a Birsk Branch of Federal State Budgetary Educational Establishment of Higher Education Bashkir State University   (Russian Federation)

Author keywords

Concave convex nonlinearity; Fibering approach; p Laplacian

Indexed keywords

BIFURCATION (MATHEMATICS); BOUNDARY VALUE PROBLEMS; DEFORMATION; INTEGRAL EQUATIONS; LAPLACE TRANSFORMS; PARAMETER ESTIMATION; PROBLEM SOLVING; SET THEORY; SPECTRUM ANALYSIS;

CONCAVE-CONVEX NONLINEARITY; DISJOINT SETS; FIBERING APPROACH; P-LAPLACIAN;

NONLINEAR SYSTEMS;

EID: 14544298283     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2004.10.022     Document Type: Article

References (25)

1. A. Ambrosetti, J.G. Azorero, and I. Peral Existence and multiplicity results for some nonlinear elliptic equations a survey Dedicated to the memory of Gaetano Fichera (Italian), Rend. Mat. Appl. 20 7 2000 167 198
2. A. Ambrosetti, H. Brezis, and G. Cerami Combined effect of concave and convex nonlinearities in some elliptic problems J. Funct. Anal. 122 1994 519 543
3. A. Ambrosetti, and P.H. Rabinowitz Dual variational methods in critical point theory and applications J. Funct. Anal. 14 1973 349 381
4. T. Bartsch, and M. Willem On an elliptic equation with concave and convex nonlinearities Proc. Amer. Math. Soc. 123 11 1995 3555 3561
5. L. Boccardo, M. Escobedo, and I. Peral A Dirichlet problem involving critical exponents Nonlinear Anal. 24 11 1995 1639 1648
6. D.C. Clark A variant of the Ljusternik-Schnirelmann theory Indiana Univ. Math. J. 22 1972 65 74
7. C.V. Coffman A minimum-maximum principle for a class of nonlinear integral equations J. Analyse. Math. 22 1969 391 419
8. S. Coleman, V. Glazer, and A. Martin Action minima among solution to a class of Euclidean scalar field equations Comm. Math. Phys. 58 2 1978 211 221
9. P. Drábek, Strongly nonlinear degenerated and singular elliptic problems, Nonlinear partial differential equations (Fes, 1994), 112-146, Pitman Res. Notes Math. Ser., 343, Longman, Harlow, 1996.
10. H. Egnell Elliptic boundary value problems with singular coefficients and critical nonlinearities Indiana Univ. Math. J. 38 2 1989 235 251
11. J. Garcia Azorero, J. Manfredi, and I. Peral Sobolev versus Hölder local minimizes and global multiplicity for some quasilinear elliptic equations Commun. Contemp. Math. 2 3 2000 385 404
12. J. Garcia Azorero, and I. Peral Alonso Multiplicity of solutions for elliptic problems with critical exponent or with a nonsymmetric term Trans. Amer. Math. Soc. 323 2 1991 877 895
13. Ya.Sh. Il'yasov Nonlocal investigations of bifurcations for solutions of nonlinear elliptic equations Izv. Russ. Ac. N. Ser. Mat. 66 6 2002 19 48
14. Y. Il'yasov On positive solutions of indefinite elliptic equations C. R. Acad. Sci., Paris 333 1 2001 533 538
15. Ya.Sh. Il'yasov On a procedure of projective fibering of functionals on Banach spaces Proc. Steklov Inst. Math. 232 2001 150 156
16. Ya.Sh. Il'yasov A nonlocal study of families of elliptic equations with convex-concave nonlinearities Doklady Akad. Nauk 392 2 2003 603 606 Doklady Math. 68(2) (2003) 258-261
17. M.A. Krasnosel'skii, Topological Methods in the Theory of Nonlinear Integral Equations, Pergamon Press, The Macmillan Co., New York, 1964, pp. 395.
18. G.M. Lieberman Boundary regularity for solutions of degenerate elliptic equations Nonlinear Anal. 12 11 1988 1203 1219
19. P.L. Lions The concentration-compactness principle in the calculus of variations. The limit case Revista Mat. Iberoamer. 1 1985 145 201 1 (1985) 45-120
20. S.I. Pohozaev On an approach to nonlinear equations Doklady Acad. Sci. USSR 247 1979 1327 1331
21. S.I. Pohozaev On the method of fibering a solution in nonlinear boundary value problems Proc. Stekl. Ins. Math. 192 1990 157 173
22. M. Struwe Variational Methods, Application to Nonlinear Partial Differential Equations and Hamiltonian Systems 1996 Springer Berlin, Heidelberg, New York
23. P. Tolksdorf Regularity for a more general class of quasilinear elliptic equations J. Differential Equations 51 1 1984 126 150
24. N.S. Trudinger On Harnack type inequalities and their application to quasilinear elliptic equations Comm. Pure Appl. Math. 20 1967 721 747
25. L. Véron Première valeur propre non nulle du p-laplacien et équations quasilinéaires elliptiques sur une varié té riemannienne compacte C. R. Acad. Sci., Paris 314 1992 271 276