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Filippo Cammaroto, Francesca Faraci (2012)
Annales Polonici Mathematici
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We deal with some Dirichlet problems involving a nonlocal term. The existence of two nonzero, nonnegative solutions is achieved by applying a recent result by Ricceri.
Martin Schechter (1992)
Annales Polonici Mathematici
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We show that one can drop an important hypothesis of the saddle point theorem without affecting the result. We then show how this leads to stronger results in applications.
Robert Altmann (2014)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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This paper develops a framework to include Dirichlet boundary conditions on a subset of the boundary which depends on time. In this model, the boundary conditions are weakly enforced with the help of a Lagrange multiplier method. In order to avoid that the ansatz space of the Lagrange multiplier depends on time, a bi-Lipschitz transformation, which maps a fixed interval onto the Dirichlet boundary, is introduced. An inf-sup condition as well as existence results are presented for a class...
G. A. Afrouzi, A. Hadjian, S. Heidarkhani (2013)
Annales Polonici Mathematici
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We prove the existence of at least one non-trivial solution for Dirichlet quasilinear elliptic problems. The approach is based on variational methods.
Giovanni Anello, Giuseppe Cordaro (2004)
Annales Polonici Mathematici
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We establish an existence theorem for a Dirichlet problem with homogeneous boundary conditions by using a general variational principle of Ricceri.
Currie, Sonja, Love, Anne D. (2010)
Advances in Difference Equations [electronic only]
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Sylwia Barnaś (2014)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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In this paper we study the nonlinear Dirichlet problem involving p(x)-Laplacian (hemivariational inequality) with nonsmooth potential. By using nonsmooth critical point theory for locally Lipschitz functionals due to Chang [6] and the properties of variational Sobolev spaces, we establish conditions which ensure the existence of solution for our problem.
H. J. Bremermann (1967)
Colloquium Mathematicae
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Agarwal, Ravi P., Perera, Kanishka, O'Regan, Donal (2005)
Advances in Difference Equations [electronic only]
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Dagmar Medková (2008)
Applicationes Mathematicae
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The Dirichlet problem for the Laplace equation for a planar domain with piecewise-smooth boundary is studied using the indirect integral equation method. The domain is bounded or unbounded. It is not supposed that the boundary is connected. The boundary conditions are continuous or p-integrable functions. It is proved that a solution of the corresponding integral equation can be obtained using the successive approximation method.
Candito, Pasquale, D'aguì, Giuseppina (2010)
Advances in Difference Equations [electronic only]
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E.B. Davies (1984/85)
Mathematische Zeitschrift
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Ali I. Abdul-Latif (1978)
Collectanea Mathematica
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David Krejčiřík (2008)
ESAIM: Control, Optimisation and Calculus of Variations
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We consider the Laplacian in a domain squeezed between two parallel curves in the plane, subject to Dirichlet boundary conditions on one of the curves and Neumann boundary conditions on the other. We derive two-term asymptotics for eigenvalues in the limit when the distance between the curves tends to zero. The asymptotics are uniform and local in the sense that the coefficients depend only on the extremal points where the ratio of the curvature radii of the Neumann boundary to the...
Jiang, Liqun, Zhou, Zhan (2008)
Advances in Difference Equations [electronic only]
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David Krejčiřík (2009)
ESAIM: Control, Optimisation and Calculus of Variations
Similarity:
We consider the laplacian in a domain squeezed between two parallel curves in the plane, subject to Dirichlet boundary conditions on one of the curves and Neumann boundary conditions on the other. We derive two-term asymptotics for eigenvalues in the limit when the distance between the curves tends to zero. The asymptotics are uniform and local in the sense that the coefficients depend only on the extremal points where the ratio of the curvature radii of the Neumann boundary to the Dirichlet...