An Existence Analysis for Nonlinear Boundary Value Problems

Abstract

Previous article Next article An Existence Analysis for Nonlinear Boundary Value ProblemsJohn LockerJohn Lockerhttps://doi.org/10.1137/0119018PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] Stephen Bancroft, , Jack K. Hale and , Daniel Sweet, Alternative problems for nonlinear functional equations, J. Differential Equations, 4 (1968), 40–56 10.1016/0022-0396(68)90047-8 MR0220118 0159.20001 CrossrefISIGoogle Scholar[2] Robert G. Bartle, Singular points of functional equations, Trans. Amer. Math. Soc., 75 (1953), 366–384 MR0058859 0051.34502 CrossrefISIGoogle Scholar[3] Lamberto Cesari, Functional analysis and Galerkin's method, Michigan Math. J., 11 (1964), 385–414 10.1307/mmj/1028999194 MR0173839 0192.23702 CrossrefGoogle Scholar[4] Lamberto Cesari, A nonlinear problem in potential theory, Michigan Math. J., 16 (1969), 3–20 10.1307/mmj/1029000160 MR0280730 0176.41102 CrossrefISIGoogle Scholar[5] Lamberto Cesari, Functional analysis and periodic solutions of nonlinear differential equations, Contributions to Differential Equations, 1 (1963), 149–187, John Wiley, New York MR0151678 0132.07101 Google Scholar[6] Earl A. Coddington and , Norman Levinson, Theory of ordinary differential equations, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1955xii+429 MR0069338 0064.33002 Google Scholar[7] Jane Cronin, Fixed points and topological degree in nonlinear analysis, Mathematical Surveys, No. 11, American Mathematical Society, Providence, R.I., 1964xii+198 MR0164101 0117.34803 Google Scholar[8] Jane Cronin, Branch points of solutions of equations in Banach space, Trans. Amer. Math. Soc., 69 (1950), 208–231 MR0040578 0041.23701 CrossrefISIGoogle Scholar[9] Nelson Dunford and , Jacob T. Schwartz, Linear Operators. I. General Theory, With the assistance of W. G. Bade and R. G. Bartle. Pure and Applied Mathematics, Vol. 7, Interscience Publishers, Inc., New York, 1958xiv+858, and part II MR0117523 0084.10402 Google Scholar[10] Israel Halperin, Closures and adjoints of linear differential operators, Ann. of Math. (2), 38 (1937), 880–919 MR1503380 0018.36603 CrossrefGoogle Scholar[11] Philip Hartman, Ordinary differential equations, John Wiley & Sons Inc., New York, 1964xiv+612 MR0171038 0125.32102 Google Scholar[12] John Locker, An existence analysis for nonlinear equations in Hilbert space, Trans. Amer. Math. Soc., 128 (1967), 403–413 MR0215142 0156.15802 CrossrefISIGoogle Scholar[13] L. Nirenberg, Functional analysis, New York University Lectures, 1960–1961 Google Scholar[14] J. Schwartz, Perturbations of spectral operators, and applications. I. Bounded perturbations, Pacific J. Math., 4 (1954), 415–458 MR0063568 0056.34901 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Nonlinear Analysis Cross Ref Existence of solutions to nonselfadjoint boundary value problems for ordinary differential equationsNonlinear Analysis: Theory, Methods & Applications, Vol. 9, No. 11 Cross Ref Equations with unbounded nonlinearitiesNonlinear Analysis: Theory, Methods & Applications, Vol. 4, No. 6 Cross Ref Nonlinear boundary value problems and operators TT∗Journal of Differential Equations, Vol. 28, No. 1 Cross Ref The Generalized Green's Function for Regular Ordinary Differential Subspaces in L2[a,b] ⊕ L2[a,b] Cross Ref The generalized Green’s function for an 𝑛th order linear differential operator1 January 1977 | Transactions of the American Mathematical Society, Vol. 228, No. 0 Cross Ref Annotated Bibliography on Generalized Inverses and Applications Cross Ref On the Generalized Emden–Fowler EquationJames S. W. Wong18 July 2006 | SIAM Review, Vol. 17, No. 2AbstractPDF (2380 KB)On constructing least squares solutions to two-point boundary value problems1 January 1975 | Transactions of the American Mathematical Society, Vol. 203, No. 0 Cross Ref An iteration scheme for boundary value/alternative problemsNumerische Mathematik, Vol. 23, No. 3 Cross Ref Large nonlinearities and monotonicityArchive for Rational Mechanics and Analysis, Vol. 48, No. 2 Cross Ref Functional analysis and boundary value problems22 August 2006 Cross Ref Volume 19, Issue 1| 1970SIAM Journal on Applied Mathematics History Submitted:26 August 1969Published online:12 July 2006 InformationCopyright © 1970 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0119018Article page range:pp. 199-207ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics