- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2011 (2011), Article ID 981401, 9 pages
Asymptotic Formula for Oscillatory Solutions of Some Singular Nonlinear Differential Equation
Department of Mathematics, Faculty of Science, Palacký University, 17. Listopadu 12, 771 46 Olomouc, Czech Republic
Received 28 October 2010; Revised 31 March 2011; Accepted 2 May 2011
Academic Editor: Yuri V. Rogovchenko
Copyright © 2011 Irena Rachůnková and Lukáš Rachůnek. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- V. Bongiorno, L. E. Scriven, and H. T. Davis, “Molecular theory of fluid interfaces,” Journal of Colloid and Interface Science, vol. 57, pp. 462–475, 1967.
- H. Gouin and G. Rotoli, “An analytical approximation of density profile and surface tension of microscopic bubbles for Van der Waals fluids,” Mechanics Research Communications, vol. 24, pp. 255–260, 1997.
- J. D. Van Der Waals and R. Kohnstamm, Lehrbuch der Thermodynamik, vol. 1, Leipzig, Germany, 1908.
- P. C. Fife, Mathematical Aspects of Reacting and Diffusing Systems, vol. 28 of Lecture Notes in Biomathematics, Springer, Berlin, Germany, 1979.
- R. A. Fischer, “The wave of advance of advantegeous genes,” Journal of Eugenics, vol. 7, pp. 355–369, 1937.
- F. F. Abraham, Homogeneous Nucleation Theory, Academies Press, New York, NY, USA, 1974.
- A. P. Linde, Particle Physics and Inflationary Cosmology, Harwood Academic, Chur, Switzerland, 1990.
- G. H. Derrick, “Comments on nonlinear wave equations as models for elementary particles,” Journal of Mathematical Physics, vol. 5, pp. 1252–1254, 1964.
- F. Dell'Isola, H. Gouin, and G. Rotoli, “Nucleation of spherical shell-like interfaces by second gradient theory: numerical simulations,” European Journal of Mechanics, vol. 15, no. 4, pp. 545–568, 1996.
- G. Kitzhofer, O. Koch, P. Lima, and E. Weinmüller, “Efficient numerical solution of the density profile equation in hydrodynamics,” Journal of Scientific Computing, vol. 32, no. 3, pp. 411–424, 2007.
- P. M. Lima, N. V. Chemetov, N. B. Konyukhova, and A. I. Sukov, “Analytical-numerical investigation of bubble-type solutions of nonlinear singular problems,” Journal of Computational and Applied Mathematics, vol. 189, no. 1-2, pp. 260–273, 2006.
- H. Berestycki, P. L. Lions, and L. A. Peletier, “An ODE approach to the existence of positive solutions for semilinear problems in ,” Indiana University Mathematics Journal, vol. 30, no. 1, pp. 141–157, 1981.
- D. Bonheure, J. M. Gomes, and L. Sanchez, “Positive solutions of a second-order singular ordinary differential equation,” Nonlinear Analysis: Theory, Methods & Appplications, vol. 61, no. 8, pp. 1383–1399, 2005.
- M. Conti, L. Merizzi, and S. Terracini, “Radial solutions of superlinear equations in , part I: a global variational approach,” Archive for Rational Mechanics and Analysis, vol. 153, no. 4, pp. 291–316, 2000.
- I. Rachůnková and J. Tomeček, “Bubble-type solutions of nonlinear singular problems,” Mathematical and Computer Modelling, vol. 51, no. 5-6, pp. 658–669, 2010.
- I. Rachůnková and J. Tomeček, “Strictly increasing solutions of a nonlinear singular differential equation arising in hydrodynamics,” Nonlinear Analysis: Theory, Methods & Appplications, vol. 72, no. 3-4, pp. 2114–2118, 2010.
- I. Rachůnková and J. Tomeček, “Homoclinic solutions of singular nonautonomous second-order differential equations,” Boundary Value Problems, vol. 2009, Article ID 959636, 21 pages, 2009.
- I. Rachůnková, J. Tomeček, and J. Stryja, “Oscillatory solutions of singular equations arising in hydrodynamics,” Advances in Difference Equations, vol. 2010, Article ID 872160, 13 pages, 2010.
- I. Rachůnková, L. Rachůnek, and J. Tomeček, “Existence of oscillatory solutions of singular nonlinear differential equations,” Abstract and Applied Analysis, vol. 2011, Article ID 408525, 20 pages, 2011.
- I. Kiguradze, Some Singular Boundary Value Problems for Ordinary Differential Equations, ITU, Tbilisi, Georgia, 1975.