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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.
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. ...
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.
Marek Galewski (2008)
Annales Polonici Mathematici
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Aleksandra Orpel (2005)
Colloquium Mathematicae
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We discuss the existence of solutions for a certain generalization of the membrane equation and their continuous dependence on function parameters. We apply variational methods and consider the PDE as the Euler-Lagrange equation for a certain integral functional, which is not necessarily convex and coercive. As a consequence of the duality theory we obtain variational principles for our problem and some numerical results concerning approximation of solutions.
Aleksandra Orpel (2004)
Banach Center Publications
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We investigate the existence of solutions for the Dirichlet problem including the generalized balance of a membrane equation. We present a duality theory and variational principle for this problem. As one of the consequences of the duality we obtain some numerical results which give a measure of a duality gap between the primal and dual functional for approximate solutions.
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.
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.
Śladkowska, Janina (2015-11-13T13:54:55Z)
Acta Universitatis Lodziensis. Folia Mathematica
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Frédéric Bayart (2004)
Acta Arithmetica
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H. M. Bui, D. R. Heath-Brown (2010)
Acta Arithmetica
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Adrian Królak (2013)
Bulletin of the Polish Academy of Sciences. Mathematics
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We consider some variational principles in the spaces C*(X) of bounded continuous functions on metrizable spaces X, introduced by M. M. Choban, P. S. Kenderov and J. P. Revalski. In particular we give an answer (consistent with ZFC) to a question stated by these authors.
Jan Sokołowski (1987)
Banach Center Publications
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Jean Ollagnier, Didier Pinchon (1982)
Studia Mathematica
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D. Bouafia, T. Moussaoui, D. O’Regan (2016)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
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In this paper we study the existence of nontrivial solutions for a nonlinear boundary value problem posed on the half-line. Our approach is based on Ekeland’s variational principle.
Kohji Matsumoto, Hirofumi Tsumura (2006)
Acta Arithmetica
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Hochmuth, Reinhard (1996)
Annales Academiae Scientiarum Fennicae. Series A I. Mathematica
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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.
A. Mallik (1981)
Acta Arithmetica
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Hongfen Yuan, Valery V. Karachik (2022)
Czechoslovak Mathematical Journal
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Applying the method of normalized systems of functions we construct solutions of the generalized Dirichlet problem for the iterated slice Dirac operator in Clifford analysis. This problem is a natural generalization of the Dirichlet problem.
Renate McLaughlin (1973)
Colloquium Mathematicae
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Zhefeng Xu, Wenpeng Zhang (2007)
Acta Arithmetica
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Gabriele Bonanno, Giovanni Molica Bisci, Vicenţiu Rădulescu (2012)
ESAIM: Control, Optimisation and Calculus of Variations
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Under an appropriate oscillating behaviour either at zero or at infinity of the nonlinear term, the existence of a sequence of weak solutions for an eigenvalue Dirichlet problem on the Sierpiński gasket is proved. Our approach is based on variational methods and on some analytic and geometrical properties of the Sierpiński fractal. The abstract results are illustrated by explicit examples.