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  • 1
    Electronic Resource
    Electronic Resource
    L p-perturbations of second order linear differential equations (1975)
    Springer
    Mathematische Annalen 215 (1975), S. 23-34 
    Details
    ISSN: 1432-1807
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01351788
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    The equivalence of strict convexity and injectivity of the gradient in bounded level sets (1991)
    Springer
    Mathematical programming 51 (1991), S. 273-278 
    Details
    ISSN: 1436-4646
    Keywords: Convexity ; injectivity ; generalized gradient ; supporting hyperplane ; affine invariance
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract It is shown that Lipschitzian functions are strictly convex if and only if their generalized gradients are disjoint at distinct interior points of a given bounded level set.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01586939
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  • 3
    Electronic Resource
    Electronic Resource
    On the Kolodner-Coffman method for the uniqueness problem of Emden-Fowler BVP (1990)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 41 (1990), S. 79-104 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract This paper surveys the Kolodner-Coffman method which has been applied very successfully by many authors to obtain uniqueness theorems for boundary value problems for differential equations of Emden-Fowler type. We recast some of the arguments in the language of Sturm's oscillation theory for linear second-order differential equations. The clarification provided by the new perspective enables us to improve several known results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00946076
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    Paper (German National Licenses)
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  • 4
    Electronic Resource
    Electronic Resource
    Semilinear elliptic problems in annular domains (1989)
    Springer
    Zeitschrift für angewandte Mathematik und Physik 40 (1989), S. 245-257 
    Details
    ISSN: 1420-9039
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Description / Table of Contents: Zusammenfassung Mit Hilfe eines Schiessverfahrens wird die Existenz von Lösungen nichtlinearer Probleme der Form Δu+f(r, u)=0 in ringförmigen Gebieten nachgewiesen, die verschiedenen Randbedingungen genügen. Es wird auch ihre Eindeutigkeit untersucht. Diese Arbeit verallgemeinert gewisse Ergebnisse von Bandle, Coffman und Marcus.
    Abstract: Résumé On utilise une méthode de tir pour établir l'existence de solutions de problèmes non linéaires du type Δu+f(r, u)=0 dans des anneaux, vérifiant différentes conditions aux limites. Ensuite on discute l'unicité de ces solutions. Ce travail généralise certains résultats de Bandle, Coffman et Marcus.
    Notes: Abstract The method of shooting is used to establish existence of positive radially symmetric solutions to nonlinear elliptic equations of the form Δu+f(r, u)=0 on annular regionsa〈r=|x|〈b inR N , satisfying Dirichlet or Neumann conditions on the boundary. This extends recent work done by Bandle, Coffman and Marcus. A result concerning uniqueness of such solutions is also extended.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00945001
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  • 5
    Electronic Resource
    Electronic Resource
    Uniqueness of positive solutions of Δu−u+up=0 in Rn (1989)
    Springer
    Archive for rational mechanics and analysis 105 (1989), S. 243-266 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract We establish the uniqueness of the positive, radially symmetric solution to the differential equation Δu−u+up=0 (with p〉1) in a bounded or unbounded annular region in R n for all n≧1, with the Neumann boundary condition on the inner ball and the Dirichlet boundary condition on the outer ball (to be interpreted as decaying to zero in the case of an unbounded region). The regions we are interested in include, in particular, the cases of a ball, the exterior of a ball, and the whole space. For p=3 and n=3, this a well-known result of Coffman, which was later extended by McLeod & Serrin to general n and all values of p below a certain bound depending on n. Our result shows that such a bound on p is not needed. The basic approach used in this work is that of Coffman, but several of the principal steps in the proof are carried out with the help of Sturm's oscillation theory for linear second-order differential equations. Elementary topological arguments are widely used in the study.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00251502
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  • 6
    Electronic Resource
    Electronic Resource
    Uniqueness results for some nonlinear initial and boundary value problems (1988)
    Springer
    Archive for rational mechanics and analysis 102 (1988), S. 45-56 
    Details
    ISSN: 1432-0673
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract In the first part of this article a uniqueness theorem is presented for nonlinear initial value problems of the type (*) $$dx/dt{\text{ = }}\phi (x){\text{ }} + {\text{ }}p(t),{\text{ }}t 〉 0;{\text{ }}x(0){\text{ = 0}};$$ where p is a real-valued continuous function which may change sign near the origin. The theorem is subsequently applied to establish a result related to the uniqueness of nonnegative nontrivial radial solutions of nonlinear boundary value problems of the type (**) $$\nabla \cdot {\text{(}}A{\text{(}}\left| {\nabla u} \right|{\text{) }}\nabla u{\text{ + }}f{\text{(}}u{\text{) = 0, }}x \in R^n {\text{; }}\mathop {\lim }\limits_{x \to \infty } {\text{ }}u{\text{(}}x{\text{) = 0;}}$$ where A is a positive continuous function such that the product pA(p) is monotone. The class of equations (**) includes the mean curvature equation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00250923
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    Paper (German National Licenses)
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  • 7
    Electronic Resource
    Electronic Resource
    Singular Sturm—Liouville problems with nonnegative and indefinite weights (1984)
    Springer
    Monatshefte für Mathematik 97 (1984), S. 177-189 
    Details
    ISSN: 1436-5081
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract This article is concerned with the oscillatory properties of the eigenfunctions of a class of singular Sturm—Liouville problems—(p y′)′+q y=λw y on (a, b), where the weight functionw vanishes on a subinterval of positive measure, or where the weight functionw changes sign on (a, b).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01299145
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    Paper (German National Licenses)
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