| 1. |
- Arnarson, Teitur, et al.
(author)
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A PDE approach to regularity of solutions to finite horizon optimal switching problems
- 2009
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In: Nonlinear Analysis. - : Elsevier BV. - 0362-546X .- 1873-5215. ; 71:12, s. 6054-6067
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Journal article (peer-reviewed)abstract
- We study optimal 2-switching and n-switching problems and the corresponding system of variational inequalities. We obtain results on the existence of viscosity solutions for the 2-switching problem for various setups when the cost of switching is non-deterministic. For the n-switching problem we obtain regularity results for the solutions of the variational inequalities. The solutions are C-l,C-l-regular away for the free boundaries of the action sets.
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| 2. |
- Björn, Anders, et al.
(author)
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Nonlinear balayage on metric spaces
- 2009
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In: Nonlinear Analysis. - : Elsevier BV. - 0362-546X .- 1873-5215. ; 71:5-6, s. 2153-2171
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Journal article (peer-reviewed)abstract
- We develop a theory of balayage on complete doubling metric measure spaces supporting a Poincaré inequality. In particular, we are interested in continuity and p-harmonicity of the balayage. We also study connections to the obstacle problem. As applications, we characterize regular boundary points and polar sets in terms of balayage.
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| 3. |
- Enstedt, M., et al.
(author)
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Existence of a solution to Hartree-Fock equations with decreasing magnetic fields
- 2008
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In: Nonlinear Analysis. - : Elsevier BV. - 0362-546X .- 1873-5215. ; 69:7, s. 2125-2141
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Journal article (peer-reviewed)abstract
- In the presence of an external magnetic field, we prove existence of a ground state within the Hartree-Fock theory of atoms and molecules. The ground state exists provided the magnetic field decreases at infinity and the total charge Z of K nuclei exceeds N - 1, where N is the number of electrons. In the opposite direction, no ground state exists if N > ; 2Z + K.
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| 4. |
- Jönsson, Ulf T., et al.
(author)
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Analysis and computation of limit cycles for systems with separable nonlinearities
- 2008
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In: Nonlinear Analysis. - : Elsevier BV. - 0362-546X .- 1873-5215. ; 69:12, s. 4674-4693
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Journal article (peer-reviewed)abstract
- The variational system obtained by linearizing a dynamical system along a limit cycle is always non-invertible. This follows because the limit cycle is only a unique modulo time translation. It is shown that questions such as uniqueness, robustness, and computation of limit cycles can be addressed using a right inverse of the variational system. Small gain arguments are used in the analysis.
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| 5. |
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| 6. |
- Lindgren, Erik, et al.
(author)
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A free boundary problem for the Laplacian with a constant Bernoulli-type boundary condition
- 2007
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In: Nonlinear Analysis. - : Elsevier BV. - 0362-546X .- 1873-5215. ; 67:8, s. 2497-2505
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Journal article (peer-reviewed)abstract
- We study a free boundary problem for the Laplace operator, where we impose a Bernoulli-type boundary condition. We show that there exists a solution to this problem. We use A. Beurling's technique, by defining two classes of sub- and super-solutions and a Perron argument. We try to generalize here a previous work of A. Henrot and H. Shahgholian. We extend these results in different directions.
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| 7. |
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| 8. |
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| 9. |
- Ringkvist, Mattias, et al.
(author)
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On Dynamical Behaviour of FitzHugh-Nagumo Systems : revisited
- 2009
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In: Nonlinear Analysis. - : Elsevier. - 0362-546X .- 1873-5215. ; 71:7-8, s. 2667-2687
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Journal article (peer-reviewed)abstract
- The purpose of this paper is to analyse a general form of the FitzHugh–Nagumo model as completely as possible. The main result is that no more than two limit cycles can be bifurcated from the unique fixed point via Hopf bifurcation, and there exist parameters such that this upper bound is attained. For these parameters, the stability of the inner and outer cycle, together with the unique fixed point is also established. The results are approached through Lyapunov coefficients and rely on a theorem by Andronov and Aleksandrovic [A.A. Andronov, A.A. Aleksandrovic, Theory of Bifurcations of Dynamical System on a Plane, Wiley, 1971]. Based on singular perturbation theory a sufficient condition for existence of a unique stable limit cycle is given under certain assumptions.
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| 10. |
- Sjödin, Tomas
(author)
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On the structure of partial balayage
- 2007
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In: Nonlinear Analysis. - : Elsevier BV. - 0362-546X .- 1873-5215. ; 67:1, s. 94-102
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Journal article (peer-reviewed)abstract
- We define partial balayage, construct it with classical potential-theoretic methods and establish the so called structure formula in full generality. Finally we give a stochastic construction of partial balayage.
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