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Article

Title: Differential equations at resonance (English)
Author: O'Regan, Donal
Language: English
Journal: Commentationes Mathematicae Universitatis Carolinae
ISSN: 0010-2628 (print)
ISSN: 1213-7243 (online)
Volume: 36
Issue: 4
Year: 1995
Pages: 673-694
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Category: math
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Summary: New existence results are presented for the two point singular ``resonant'' boundary value problem $\frac{1}{p}(py')'+r y+\lambda_m qy=f(t,y,py')$ a.e\. on $[0,1]$ with $y$ satisfying Sturm Liouville or Periodic boundary conditions. Here $\lambda_m$ is the $(m+1)^{st}$ eigenvalue of $\frac{1}{pq} [(pu')' +rpu] +\lambda u=0$ a.e\. on $[0,1]$ with $u$ satisfying Sturm Liouville or Periodic boundary data. (English)
Keyword: boundary value problems
Keyword: resonance
Keyword: existence
MSC: 34B15
MSC: 34B24
idZBL: Zbl 0843.34029
idMR: MR1378689
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Date available: 2009-01-08T18:20:54Z
Last updated: 2012-04-30
Stable URL: http://hdl.handle.net/10338.dmlcz/118795
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Reference: [1] Atkinson F.V.: Discrete and continuous boundary problems.Academic Press, New York, 1964. Zbl 0169.10601, MR 0176141
Reference: [2] Atkinson F.V., Everitt W.N., Zettl A.: Regularization of a Sturm Liouville problem with an interior singularity.Diff. Int. Eq. 1 (1988), 213-221. Zbl 0715.34043, MR 0922562
Reference: [3] Bobisud L.E., O'Regan D.: Positive solutions for a class of nonlinear singular boundary value problems at resonance.Jour. Math. Anal. Appl. 184 (1994), 263-284. Zbl 0805.34019, MR 1278388
Reference: [4] Cesari L., Kannan R.: Existence of solutions of a nonlinear differential equation.Proc. Amer. Math. Soc. 88 (1983), 605-613. Zbl 0529.34005, MR 0702284
Reference: [5] Fonda A., Mawhin J.: Quadratic forms, weighted eigenfunctions and boundary value problems for nonlinear second order ordinary differential equations.Proc. Royal Soc. Edinburgh 112A (1989), 145-153. Zbl 0677.34022, MR 1007541
Reference: [6] Iannacci R., Nkashama M.N.: Unbounded perturbations of forced second order ordinary differential equations at resonance.Jour. Diff. Eq. 69 (1987), 289-309. Zbl 0627.34008, MR 0903389
Reference: [7] Iannacci R., Nkashama M.N.: Nonlinear two point boundary value problems at resonance without Landesman- Lazer conditions.Proc. Amer. Math. Soc. 106 (1989), 943-952. MR 1004633
Reference: [8] Mawhin J., Ward J.R.: Periodic solutions of some forced Lienard differential equations at resonance.Archiv der Math. 41 (1983), 337-351. Zbl 0537.34037, MR 0731606
Reference: [9] Mawhin J., Ward J.R., Willem M.: Necessary and sufficient conditions for the solvability of a nonlinear two point boundary value problem.Proc. Amer. Math. Soc. 93 (1985), 667-674. Zbl 0559.34014, MR 0776200
Reference: [10] Mawhin J., Willem M.: Critical point theory and Hamiltonian systems.Springer Verlag, New York, 1989. Zbl 0676.58017, MR 0982267
Reference: [11] Mawhin J., Omano W.: Two point boundary value problems for nonlinear perturbations of some singular linear differential equations at resonance.Comment. Math. Univ. Carolinae 30 (1989), 537-550. MR 1031871
Reference: [12] Naimark M.A.: Linear differential operators Part II.Ungar Publ. Co., London, 1968. Zbl 0227.34020, MR 0262880
Reference: [13] Nkashama M.N., Santanilla J.: Existence of multiple solutions of some nonlinear boundary value problems.Jour. Diff. Eq. 84 (1990), 148-164. MR 1042663
Reference: [14] O'Regan D.: Singular Sturm Liouville problems and existence of solutions to singular nonlinear boundary value problems.Nonlinear Anal. 20 (1993), 767-779. Zbl 0780.34017
Reference: [15] O'Regan D.: Solvability of some two point boundary value problems of Dirichlet, Neumann or Periodic type.Dynamic Systems and Appl. 2 (1993), 163-182. Zbl 0785.34025, MR 1226995
Reference: [16] O'Regan D.: Existence principles for second order nonresonant boundary value problems.Jour. Appl. Math. Stoch. Anal. 7 (1994), 487-507. Zbl 0819.34019, MR 1310923
Reference: [17] O'Regan D.: Carathéodory theory of nonresonant second order boundary value problems.to appear. Zbl 0870.34028
Reference: [18] Ramas M., Sanchez L.: Variational elliptic problems involving noncoercive functionals.Proc. Roy. Soc. Edinburgh 112A (1989), 177-185. MR 1007543
Reference: [19] Sanchez L.: Positive solutions for a class of semilinear two point boundary value problems.Bull. Aust. Math. Soc. 45 (1992), 439-451. Zbl 0745.34017, MR 1165150
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