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Displaying similar documents to “Multiple solutions for some Dirichlet problems with nonlocal terms”

Non-trivial solutions for a two-point boundary value problem

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.

Triple solutions for a Dirichlet boundary value problem involving a perturbed discretep(k)-Laplacian operator

Mohsen Khaleghi Moghadam, Johnny Henderson (2017)

Open Mathematics

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Triple solutions are obtained for a discrete problem involving a nonlinearly perturbed one-dimensional p(k)-Laplacian operator and satisfying Dirichlet boundary conditions. The methods for existence rely on a Ricceri-local minimum theorem for differentiable functionals. Several examples are included to illustrate the main results.

New variational principle and duality for an abstract semilinear Dirichlet problem

Marek Galewski (2003)

Annales Polonici Mathematici

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A new variational principle and duality for the problem Lu = ∇G(u) are provided, where L is a positive definite and selfadjoint operator and ∇G is a continuous gradient mapping such that G satisfies superquadratic growth conditions. The results obtained may be applied to Dirichlet problems for both ordinary and partial differential equations.

Existence and stability of solutions for semilinear Dirichlet problems

Marek Galewski (2006)

Annales Polonici Mathematici

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We provide existence and stability results for semilinear Dirichlet problems with nonlinearities satisfying some general local growth conditions. We derive a general abstract result which we then apply to prove the existence of solutions, their stability and continuous dependence on parameters for a sixth order ODE with Dirichlet type boundary data.

Growth of coefficients of universal Dirichlet series

A. Mouze (2007)

Annales Polonici Mathematici

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We study universal Dirichlet series with respect to overconvergence, which are absolutely convergent in the right half of the complex plane. In particular we obtain estimates on the growth of their coefficients. We can then compare several classes of universal Dirichlet series.

Moving Dirichlet boundary conditions

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...

Dirichlet problems without convexity assumption

Aleksandra Orpel (2005)

Annales Polonici Mathematici

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We deal with the existence of solutions of the Dirichlet problem for sublinear and superlinear partial differential inclusions considered as generalizations of the Euler-Lagrange equation for a certain integral functional without convexity assumption. We develop a duality theory and variational principles for this problem. As a consequence of the duality theory we give a numerical version of the variational principles which enables approximation of the solution for our problem. ...