Ecuaciones semilineales con espectro discreto

dc.contributorRubiano, Gustavo
dc.creatorCaicedo Contreras, José Francisco
dc.creatorCastro, Alfonso
dc.date.accessioned2021-08-20T17:38:01Z
dc.date.available2021-08-20T17:38:01Z
dc.date.created2021-08-20T17:38:01Z
dc.date.issued2012
dc.identifierhttps://repositorio.unal.edu.co/handle/unal/79984
dc.identifierUniversidad Nacional de Colombia
dc.identifierRepositorio Institucional Universidad Nacional de Colombia
dc.identifierhttps://repositorio.unal.edu.co/
dc.description.abstractEste libro está diseñado como un primer curso sobre ecuaciones diferenciales semilineales para estudiantes con conocimientos básicos de álgebra lineal, análisis matemático y ecuaciones diferenciales. El estudio del primer capítulo solamente requiere de conocimientos básicos de ecuaciones diferenciales elementales. Para el segundo capítulo se necesita manejo de las coordenadas polares y el teorema del valor intermedio. Lo anterior, más conocimiento de ecuaciones diferenciales ordinarias singulares facilitan el estudio del capítulo 3. En el capítulo métodos de orden, se usa a menudo el papel de las segundas derivadas parciales por su importancia para determinar mínimos o máximos locales. El estudio de los capítulos 5 a 8 requiere de cierta familiaridad con conceptos básicos del análisis funcional tales como la integral de Lebesgue, espacios de Hilbert y espacios Lp. (Texto tomado de la fuente).
dc.languagespa
dc.publisherUniversidad Nacional de Colombia
dc.publisherSede Bogotá
dc.publisherBogotá, Colombia
dc.relationColección textos;
dc.relationPrimera edición
dc.relationR. Adams, Sobolev spaces, Academic Press, New York, 1975.
dc.relationI. Ali and A. Castro, Positive solutions for a semilinear elliptic problem with critical exponent, Nonlinear Analysis 27 (1996), no. 3, 327– 338.
dc.relationJ. Ali, R. Shivaji, and M. Ramaswamy, Multiple positive solutions for classes of elliptic systems with combined nonlinear effects, Differential Integral Equations 19 (2006), no. 6, 669–680.
dc.relationH. Amann, Fixed point problems and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Review 18 (1976), 620–709.
dc.relationSaddle points and multiple solutions of differential equations, Math. Z. (1979), 127–166.
dc.relationH. Amann and S. A. Weiss, On the uniqueness of the topological degree, Math. Z. 130 (1973), 39–54.
dc.relationP. Bates and A. Castro, Existence and uniqueness for a variational hyperbolic systems, Nonlinear Analysis. 4 (1980), no. 6, 1151–1156.
dc.relationNecessary and sufficient conditions for existence of solutions to equations with noninvertible linear part, Rev. Colombiana.Mat. 15 (1981), no. 1, 7–23.
dc.relationV. Benci and D. Fortunato, Towards a unified field theory for classical electrodynamics, Arch. Ration. Mech. Anal. 173 (2004), no. 3, 379–414.
dc.relationV. Benci and P. Rabinowitz, Critical point theorems for indefinite functionals, Inventions math. 52 (1979), 241–273.
dc.relationA.G. Bratsos, the solution of the two dimensional sine-gordon equation using the method of lines, Journal of Computational and Applied Mathematics 206 (2007), 251–277.
dc.relationH. Brezis, Analyse Fonctionelle, Masson, 1983.
dc.relationH. Brezis and L. Nirenberg, Characterizations of the ranges of some nonlinear operators and applications to boundary value problems, Annali della Scuola Norm. Sup. di Pisa (1978), 225–236.
dc.relationR. Brooks and K. Schmitt, The contraction mapping principle and some applications, Electronic Journal of Differential Equations, Monograph (2009), 225–236.
dc.relationJ. Caicedo and A. Castro, A semilinear wave equation with derivative of nonlinearity containing multiple eigenvalues of infinite multiplicity, Contemp. Math. 208 (1997), 111–132.
dc.relationJ.F. Caicedo and A. Castro, A semilinear wave equation with smooth data and no resonance having no continuous solution, Discrete and Continuous Dynamical Systems 24 (2009), 653–658.
dc.relationJ.F. Caicedo, A. Castro, and R. Duque, Existence of solutions for a wave equation with nonmonotone nonlinearity and a small parameter, preprint (2010).
dc.relationR. Cantrell, C. Cosner, and S. Martínez, Global bifurcation of solutions to diffusive logistic equations on bounded domains subject to nonlinear boundary conditions, Proc. Roy. Soc. Edinburgh Sect. A 139 (2009), no. 1, 45.
dc.relationA. Castro, Sufficient conditions for the existence of weak solutions of the boundary value problem Lu=g(u(x ),x ) (x ∈ Ω), u(x )=0 (x ∈ ∂Ω), Rev. Colombiana Mat. (1975), no. 3, 173–187.
dc.relationHammerstein integral equations with indefinite kernel, Internet. J. Math. Sci. 1 (1978), no. 8, 187–201.
dc.relationPeriodic solutions of the forced pendulum equation, Academic Press (1980), 149–160.
dc.relationA. Castro, J. Cossio, and J.M. Neuberger, A sign changing for a superlinear Dirichlet problem, Rocky Mountain J.Math.
dc.relationA minimax principle, index of the critical point, and existence of sign changing solutions to elliptic boundary value problem, Electron. J. Differential Equations 02 (1998), 18.
dc.relationA. Castro, J. Cossio, and C.A. Velez, Existence of seven solutions for an asymptotically linear Dirichlet problem, preprint (2010).
dc.relationA. Castro and A. Kurepa, Energy analysis of a nonlinear singular diferencial equation and applications, Rev. Colombiana Mat. 21 (1987), 155–166.
dc.relationA. Castro and A. Lazer, Applications of a maximun principle, Rev.Col. de Mat. (1976).
dc.relationCritical point theory and the numbers of solutions of a nonlinear dirichlet problem, Ann. Mat. Pura Appl. 4 (1979), no. 120.
dc.relationOn periodic solutions of weakly coupled systems of differential equations, Boll. Un. Mat. Ital. B 5 (1981), no. 18, 733–742.
dc.relationA. Castro and B. Preskill, Existence of solutions for a semilinear wave equation with non-monotone nonlinearity, Discrete Contin. Dyn. Syst. 28 (2010), no. 2, 649.
dc.relationA. Castro and R. Shivaji, Non-negative solutions for a class of nonpositone problems, Proc. Royal Soc. Endinburg Sect. A 108 (1988), no. 8, 291–302.
dc.relationNon-negative solutions to a semilinear Dirichlet problem in a ball are positive and radially symmetric, Comm. in Partial Differential Equations 14 (1989), no. 8, 1091–1100.
dc.relationA. Castro and S. Unsurangsie, A semilinear wave equation with non-monotone nonlinearity, Pacific J. Math 132 (1988), no. 2, 215–225.
dc.relationS. Cingolani and M. Clapp, intertwining semiclassical bound states to a nonlinear magnetic schrodinger equation, Nonlinearity 22 (2009), no. 9, 2309–2331.
dc.relationSymmetric semiclassical states to a magnetic nonlinear schrodinger equation via equivariant morse theory, Commun. Pure Appl. Anal. 9 (2010), no. 5, 1263–1281.
dc.relationD. Clark, A variant of the Lusternik-Schnierelmann theory, Indiana Univ. Math. J. 22 (1972), 579–584.
dc.relationD. de Figueiredo, P. Lions, and R. Nusbaum, A priori and existence of positive solutions of semilinear elliptic equations, J. Math. Pures. Appl. 61 (1982), 41–63.
dc.relationP. Drabek, A. Kufner, and F. Nicolosi, Quasilinear elliptic equations with degenerations and singularities, Walter de Gruyter, Berlin, New York, 1997.
dc.relationS. Fucik, J. Necas, J. Soucek, and V. Soucek, Spectral analysis of nonlinear operators, vol. 343, Springer Verlag, 1973.
dc.relationB. Gidas, W. Ni, and L. Nirenberg, Symmetry and related properties via the maximum principle, Comm. Math. Phys. 68 (1979), 209–243.
dc.relationB. Gidas and J. Spruck, A priori bounds for positive solutions of nonlinear elliptic equations, Comm. Partial Differential Equations. 6 (1981), 883–901.
dc.relationD. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order, Springer-Verlag, 1998.
dc.relationV. Guillemin and A. Pollack, Differential Topology, Prentice Hall, Inc, 1974.
dc.relationH. Hofer, On the range of a wave operator with non-monotone nonlinearity, Math. Nachr. 106 (1982), 327–340.
dc.relationJ. Jacobsen and K. Schmitt, Radial solutions of quasilinear elliptic differential equations, Elsevier/North-Holland.
dc.relationJ. Jia and J. Huang, Krylov deferred correction accelerated method of lines transpose for parabolic problems, Journal of computational Physics 227 (2008), 1739–1753.
dc.relationD. Joseph and T. Lundgren, Quasilinear Dirichlet problems driven by positive sources, Arch. Rational Mech. Anal. 49 (1973), 241–269.
dc.relationA. Khamayseh and R. Shivaji, Evolution of bifurcation curves for semipositone problems when nonlinearities develop multiple zeroes, Appl. Math. Comput. 52 (1992), no. 2, 173–188.
dc.relationM. Krasnoselskii, Topological methods in the theory of nonlinear integral equations, Pergamon Press, London, New York, 1964.
dc.relationE. Landesman and A. Lazer, Nonlinear perturbations of elliptic boundary value problems at resonance, J. Math. Mech. 19 (1970).
dc.relationS. Lang, Real Analysis, Addisson-Wesley Publishing Company, 1983.
dc.relationA. Lazer, E. Landesman, and D. Meyers, On saddle point problems in the calculus of variations, the ritz algorithm, and monotone convergence, J. Math. Appl. 52 (1975), no. 3.
dc.relationN.G. Lloyd, Degree theory, Cambridge University Press., 1978.
dc.relationJ. Mawhin, Periodic solutions of some semilinear wave equations and systems: a survey, Chaos, Solitons, and Fractals 5 (1995), 1651– 1669.
dc.relationP. J. McKenna, On solutions of a nonlinear wave equation when the ratio of the period to the length of the interval is irrational, Proc. Amer. Math. Soc. 93 (1985), no. 1, 59–64.
dc.relationA. Miciano and R. Shivaji, Multiple positive solutions for a class of semipositone Newmann two boundary value problems, J. Math. Anal. Appl. 178 (1993), no. 1, 102–115.
dc.relationJ. Milnor, Topology from a differentiable viewpoint, Princeton University Press.
dc.relationL. Nirenberg, Topics in nonlinear functional analysis, Courant Institute Lecture Notes, New York, 1974.
dc.relationF. Pacella and T. Weth, Symmetry of solutions to semilinear elliptic equations via morse index, Proc. Amer. Math. Soc. 135, no. 6, 1753– 1762.
dc.relationR. Palais, Lusternik-Schnirelmann theory on Banach manifolds, Topology 5 (1966), 115–132.
dc.relationM. Protter and H. Weinberger, Maximun principles in differential equations, Prentice Hall, Englewood, Cliffs, N.J., 1967.
dc.relationP. Pucci and J. Serrin, A general variational identity, Indiana Univ. Math. J. 35 (1986), 681–703.
dc.relationP.H. Rabinowitz, Some global results for nonlinear eigenvalue problems, J. Funct. Anal. 7 (1971), 487–513.
dc.relationPeriodic solutions of Hamiltonian systems, Com. Pure Appl. Math. 31 (1978), 157–184.
dc.relationSome minimax theorems and applications to nonlinear partial differential equations, Nonlinear Analysis, Ac.Press 65 (1978), 161–177.
dc.relationMinimax methods in critical point theory with applications to differential equations, CBMS 65 (1985).
dc.relationM. Reed and B. Simon, Methods of modern mathematical physics, Academic Press., Inc., 1980.
dc.relationH. Royden, Real Analysis, McMillan Publishing Co., Inc., 1968.
dc.relationW. Rudin, Principles of mathematical analysis, McGraw-Hill, New York, 1976.
dc.relationReal and complex analysis, McGraw-Hill, New York, 1987.
dc.relationJ. Schwartz, Nonlinear functional analysis, Gordon Breach, New York, 1962.
dc.relationM. Willem, Density of the range of potential operators, Proc. Amer. Math. Soc. 83 (1981), no. 2, 341–344.
dc.relationP. Zhao, C. Zhong, and J. Zhu, Positive solutions for a nonhomogeneous semilinear elliptic problem with supercritical exponent, J. Math. Anal. Appl. 254 (2001), no. 2, 335–347.
dc.rightsAtribución-NoComercial-SinDerivadas 4.0 Internacional
dc.rightshttp://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rightsinfo:eu-repo/semantics/openAccess
dc.rightsDerechos Reservados al Autor, 2012
dc.titleEcuaciones semilineales con espectro discreto
dc.typeLibro


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