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Resonance problems for the one-dimensional  -Laplacian
Author(s):
Pavel
Drábek;
Stephen
B.
Robinson
Journal:
Proc. Amer. Math. Soc.
128
(2000),
755-765.
MSC (2000):
Primary 34B15
Posted:
September 9, 1999
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Abstract:
We consider resonance problems for the one dimensional  -Laplacian, and prove the existence of solutions assuming a standard Landesman-Lazer condition. Our proofs use variational techniques to characterize the eigenvalues, and then to establish the solvability of the given boundary value problem.
References:
- 1.
- A. Anane and N. Tsouli, On the second eigenvalue of the p-Laplacian, in: Nonlinear Partial Differential Equations (From a Conference in Fes, Maroc, 1994), A. Benkirane and J.-P. Gossez Ed., Pitman Research Notes in Math. 343, Longman 1996. MR 97k:35190
- 2.
- D. Arcoya and L. Orsina, Landesman-Lazer conditions and quasilinear elliptic equations, Nonlinear Analysis T.M.A. 28 (1997), 1623-1632. MR 97m:35060
- 3.
- P. Binding, P. Drábek, Y.X. Huang, On the Fredholm alternative for the
 -Laplacian, Proc. Amer. Math. Soc. 125(12) (1997), 3555-3559. MR 98b:35058 - 4.
- P.Binding, P. Drábek, Y.X. Huang, On the range of the -Laplacian, Appl. Math. Letters Vol. 10, No. 6 (1997), 77-82. MR 98g:34035
- 5.
- P. Drábek, P. Taká\v{c}, A counterexample to the Fredholm alternative for the -Laplacian, Proc. Amer. Math. Soc. 127 (1999), 1079-1087. CMP 99:06
- 6.
- P. Drábek, Solvability and bifurcations of nonlinear equations, Pitman Research Notes in Mathematics 265, Longman, Harlow, 1992. MR 94e:47084
- 7.
- K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, Berlin, Heidelberg, 1985. MR 86j:47001
- 8.
- E. M. Landesman and A. C. Lazer, Nonlinear perturbations of linear elliptic boundary value problems at resonance, J. Math. Mech. 19, 609-623 (1970). MR 42:2171
- 9.
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- 10.
- M. Struwe, Variational Methods; Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems, Springer-Verlag, New York, 1990. MR 92b:49002
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Additional Information:
Pavel
Drábek
Affiliation:
Department of Mathematics, University of West Bohemia, P.O. Box 314, 306 14 Pilsen, Czech Republic
Email:
pdrabek@kma.zcu.cz
Stephen
B.
Robinson
Affiliation:
Department of Mathematics and Computer Science, Wake Forest University, Winston-Salem, North Carolina 27109
Email:
robinson@mthcsc.wfu.edu
DOI:
10.1090/S0002-9939-99-05485-4
PII:
S 0002-9939(99)05485-4
Received by editor(s):
April 21, 1998
Posted:
September 9, 1999
Additional Notes:
The first author's research was sponsored by the Grant Agency of the Czech Republic, Project no. 201/97/0395, and partly by the Ministery of Education of the Czech Republic, Project no. VS97156.
Communicated by:
Hal L. Smith
Copyright of article:
Copyright
1999,
American Mathematical Society
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