On the solvability of Dirichlet problem for the weighted p-Laplacian

• Autorzy: Szlachtowska E.
• Języki publikacji: EN

Abstrakty

EN

The paper investigates the existence and uniqueness of weak solutions for a non-linear boundary value problem involving the weighted ρ-Laplacian. Our approach is based on variational principles and representation properties of the associated spaces.

Słowa kluczowe

EN

p-Laplacian; weak solutions; solvability

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2012
• Tom: Vol. 32, no. 4
• Strony: 775--781
• Opis fizyczny: Bibliogr. 15 poz.

Twórcy

autor

Szlachtowska E.

• AGH University of Science and Technology Faculty of Applied Mathematics al. A. Mickiewicza 30, 30-059 Krakow, Poland.,

Bibliografia

• [1] R.A. Adams, J.J.F. Fournier, Sobolev Spaces, Academic Press, 2nd. ed., 2003.
• [2] J.F. Bonder, J.D. Rossi, Existence results for the p-Laplacian with nonlinear boundary conditions, J. Math. Anal. Appl. 263 (2001), 195–223.
• [3] A.C. Cavalheiro, Existence of solutions for Dirichlet problem of some degenerate quasilinear elliptic equations, Complex Variables and Elliptic Equations 53 (2008) 2 February, 185–194.
• [4] A.C. Cavalheiro, Weighted Sobolev spaces and degenerate elliptic equations, Bol. Soc. Paran. Mat. (3s.) 26 (2008) 1–2, 117–132.
• [5] P. Cojuhari, A. Gheondea, Closed embeddings of Hilbert spaces. J. Math. Anal. Appl. 369 (2010), 60–75.
• [6] P. Cojuhari, A. Gheondea, On lifting of operators to Hilbert spaces induced by positive selfadjoint operators, J. Math. Anal. Appl. 304 (2005), 584–598.
• [7] P. Drábek, A. Kufner, F. Nicolosi, Quasilinear Elliptic Equations with Degenerations and Singularities, de Gruyter Series in Nonlinear Analysis and Applications 5, Walter de Gruyter, Berlin, 1997.
• [8] D.E. Edmunds, W.D. Evans, Spectral Theory and Differential Operators, Oxford University Press, 1987.
• [9] S. Fucík, Solvability of nonlinear equations and boundary value problems. Society of Czech. Math. Phys., Prague, 1980.
• [10] S. Fucík, A. Kufner, Nonlinear Differential Equations. Elsevier, Amsterdam, 1980.
• [11] A. Kufner, B. Opic, How to define reasonably weighted Sobolev spaces, Comment. Math. Univ. Carol. 25 (1984), 537–554.
• [12] R.C. James, Orthogonality and linear functionals in normed linear spaces, Trans. Amer. Math. Soc. 61 (1947), 265–292.
• [13] A. Lê, Eigenvalue problems for the p-Laplacian, Nonlinear Analysis 64 (2006), 1057–1099.
• [14] J.L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod et Gauthier-Villars, Paris, 1969 (Russian translation: Moscow 1972).
• [15] E. Zeidler, Nonlinear functional analysis and its applications. III: Variational methods and optimization, Springer-Verlag, New York etc., 1985.