Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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BOUNDARY VALUE PROBLEMS FOR NONLINEAR PERTURBATIONS OF VECTOR P-LAPLACIAN-LIKE OPERATORS

  • Manasevich, Raul (Departamento de Ingenieria Matermatica Universidad de Chile Santiago) ;
  • Mawhin, Jean (Jean Mawhin Institut mathematique Universite de Louvain)
  • Published : 2000.09.01
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Abstract

The aim of this paper is to obtain nonlinear operators in suitable spaces whise fixed point coincide with the solutions of the nonlinear boundary value problems ($\Phi$($\upsilon$'))'=f(t, u, u'), l(u, u') = 0, where l(u, u')=0 denotes the Dirichlet, Neumann or periodic boundary conditions on [0, T], $\Phi$: N N is a suitable monotone monotone homemorphism and f:[0, T] N N is a Caratheodory function. The special case where $\Phi$(u) is the vector p-Laplacian $\mid$u$\mid$p-2u with p>1, is considered, and the applications deal with asymptotically positive homeogeneous nonlinearities and the Dirichlet problem for generalized Lienard systems.

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References

  1. Differential and Integral Equations v.10 On the existence and multiplicity of positive solutions of the p-Laplacian with separated boundary conditions A. K. Ben-Naoum;C. De Coster
  2. Proc. Amer. Math. Soc. to appear On the Fredholm alternative for the p-Laplacian P. A. Binding;P. Drabek;Y. X. Huang
  3. Appl. Math. Letters v.10 On the range of the p-Laplacian
  4. Rocky Mountain J. Math. v.21 Steady state turbulent flow with reaction L. E. Bobisud
  5. Nonlinear Analysis T. M. A. v.10 Gneralization of Fredholm alternative for nonlinear differential operators L. Boccardo;P. Drabek;D. Giachetti;M. Kucera
  6. Nonresonance to the right of the first eigenvalue for the one-dimensional p-Laplacian M. Cuesta;J. P. Gossez;P. Omari
  7. Results in Math. to appear Multiple solutions of weakly-coupled systems with p-Laplacian operators W. Dambrosio
  8. Nonlinear Analysis T. M. A. v.23 On pairs of positive solutions for the one-dimensional p-Laplacian C. De Coster
  9. Nonlinear Functional Analysis K. Deimling
  10. Mathematical Engineering Thesis Sobre un problema cuasilineal de segundo orden Del Pino, M.
  11. The Fredholm alternative at the first eigenvalue for the one-dimensional p-Laplacian M. Del Pino;P. Drabek;R. Manasevich
  12. J. Differential Equations v.80 A homotopic deformation along p of a Leray-Schauder degree result and existence for (|$u^1$|$^p-2$)¹ + f(t,u) = 0, u(0) = u(T) = 0, p > 1 M. Del Pino;M. Elgueta;R. Manasevich
  13. Proc. Amer. Math. Soc. v.112 Multiple solutions for the p-Laplacian under global nonresonance M. Del Pino;R. Manasevich
  14. Nonlivear Analysis T. M. A. v.18 Existence and multiplicity of solutions with proscribed period for a second order quasilinear o.d.e. M. Del Pino;R. Manasevich;A. Murua
  15. Casopis pestov. mat. v.105 Ranges of a-homogeneous operators and their perturbations P. Drabek
  16. Comm. Math. Univ. Carolin v.25 Remarks on nonlivear noncoercive problems with jumping nonlinearties
  17. Rend. Ist. Mat. Univ. Trieste v.18 Solvability of boundary value problems with homogeneous ordinary differential operators
  18. Research Notes in Math. Pitman Solvability and Bifurcation on Nonlinear Equations
  19. On the closed solution to some nonhomogeneous eigenvalue problems with p-Laplacian P. Drabek;R. Manasevich
  20. Resonance problems for the one-dimensional p-Laplacian P. Drabek;S. B. Robinson
  21. A counterexample to the fredholm alternative for the p-Laplacian P. Drabek;P. Takac
  22. Rend. Ist. Mat. Univ. Trieste v.24 Periodic solutions of second order differential equations with a p-Laplacian and asymmetric nonlinearities C. Fabry;D. Fayyad
  23. Lecture Note in Math. Spectral Analysis of Nonlinear Operators S. Fucik;F. Necas;J. Soucek;V. Soucek
  24. Differential and Integral Equations v.6 Strongly nonlinear second-order ODE's with rnilateral conditions M. Garcia-Huidobro;R. Manasevich;F. Zanolin
  25. J. Differential Equations v.114 A Fredholm-like result for strongly nonlinear second order ODE's
  26. J. Comput. Appl. Math. v.52 On a pseudo Fucik spectrum for strongly nonlinear second order ODE's and an existence result
  27. J. Math. Anal. Applic. v.202 Strongly nonlinear second-order ODE's with rapidly growing terms
  28. Nonlinear Analysis T. M. A. v.28 Multiplicity of solutions for a class of nonlinear $2^nd$ order equations M. Garc'a-Huidobro;P. Ubilla
  29. Differential and Integral Equations v.6 Boundary value problems of a class of quasilinear ordinary differential equations Z. Guo
  30. J. Math. Anal. Appl. v.198 Existence and uniqueness results for some nonlinear boundary value problems D. D. Hai;S. F. Oppenheimer
  31. Proc. Roy. Soc. Edinburgh Singular boundary value problems for p-Laplacian like equations
  32. Differential and Integral Equations v.8 The existence of solutions to a class of semi-linear equations Y. X. Huang;G. Metzen
  33. Differential and Integral Equations v.4 Existence theorems for second order boundary value problems H. G. Kaper;M. Knaap;M. K. Kwong
  34. Rocky Mountain J. Math. v.23 Note on a nonlinear eigenvalue problem P. Lindqvist
  35. J. Differential Equations v.145 Periodic solutions of nonlinear systems with p-Laplacian-like operators R. Manasevich;J. Mawhin
  36. Differential and Integral Equations v.8 Positive solutions for the one-dimensional p-Laplacian R. Manasevich;F. I. Njoku;F. Zanolin
  37. Nonlinear Anal. T. M. A. v.21 Time-mappings and multiplicity of solutions for the one-dimensional p-Laplacian R. Manasevich;F. Zanolin
  38. J. Differential Equations v.12 Equivalence theorems for nonlinear operator equations and coin-cidence degree theory for some mappings in locally convex topological vector spaces J. Mawhin
  39. CBMS Regional Conf. Ser in Math. AMS. Providence v.40 Topological methods in nonlinear boundary value problems
  40. Lecture Notes in Math v.1537 Topological degree and boundary volue problems for nonlinear differential equations, in Topological Methods for Ordinary Differential Equations M. Furi(ed.);P. Zecca(ed.)
  41. SIAM J. of Math. Anal. v.24 Some general existence principles and results for (φ(y¹))¹ = qf(t,y,y¹), 0 < t < 1 D. O'Regan
  42. Nonlinear Anal. T. M. A. v.8 On certain second order ordinary differential equations associated with Sobolev-Poincare-type inequalities M. Otani
  43. Ordinary Differential Equations. Stability and Periodic Solutions N. Rouche;J. Mawhin
  44. J. Math. Anal. Appl. v.190 Mutiplicity results for the 1-dimensional generalized p-Laplacian P. Ubilla
  45. Tohoku Math. J. v.47 Boundary value problems for general second order equations and similarity solutions to the Rayleigh problem J. Wang;W. Gao;Z. Lin
  46. Nonlinear Anal. T. M. A. v.29 Nonuniform nonresonance at the first eigenvalue of the p-Laplacian M. Zhang