A general elliptic equation with intrinsic operator

• Autorzy: Motreanu Dumitru

Identyfikatory

DOI

10.7494/OpMath.2025.45.5.647

• Języki publikacji: EN

Abstrakty

EN

Existence and bound of a solution is established for a general elliptic equation with intrinsic operator subject to Dirichlet boundary condition. This provides a sufficient condition to the fundamental question if there is a solution belonging to a prescribed ball in the function space. An application deals with an equation involving a convolution product.

Słowa kluczowe

EN

nonlinear elliptic equations; intrinsic operator; convolution

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2025
• Tom: Vol. 45, no. 5
• Strony: 647--655
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Motreanu Dumitru

• University of Perpignan, Department of Mathematics, 66860 Perpignan, France

• https://orcid.org/0000-0001-7391-9534

Bibliografia

• [1] H. Brezis, Functional Analysis, Sobolev Spaces and Partial Differential Equations, Universitext, Springer, New York, 2011.
• [2] S. Carl, V.K. Le, D. Motreanu, Nonsmooth Variational Problems and Their Inequalities. Comparison Principles and Applications, Springer Monographs in Mathematics, Springer, New York, 2007.
• [3] M. Galewski, Basic Monotonicity Methods with Some Applications, Compact Textbooks in Mathematics, Birkhäuser/Springer, Cham, 2021.
• [4] R. Livrea, D. Motreanu, A. Sciammetta, Quasi-linear elliptic systems with intrinsic operators, Discrete and Continuous Dynamical Systems – Series S (2025).
• [5] G. Marino, D. Motreanu, Existence and L-estimates for elliptic equations involving convolution, Comput. Math. Methods 2 (2020), no. 5, e1103.
• [6] A.H.S. Medeiros, D. Motreanu, A problem involving competing and intrinsic operators, Sao Paulo J. Math. Sci. 18 (2024), no. 1, 300–311.
• [7] D. Motreanu, Nonlinear Differential Problems with Smooth and Nonsmooth Constraints, Mathematical Analysis and Its Applications, Academic Press, London, 2018,
• [8] D. Motreanu, V.V. Motreanu, (p, q)-Laplacian equations with convection term and a intrinsic operator, [in:] Differential and integral inequalities, Springer Optim. Appl., 151, Springer, Cham, 2019, 589–601.
• [9] D. Motreanu, V.V. Motreanu, Non-variational elliptic equations involving (p, q)-Laplacian, convection and convolution, Pure Appl. Funct. Anal. 5 (2020), no. 5, 1205–1215.
• [10] D. Motreanu, A. Sciammetta, On a Neumann problem with an intrinsic operator, Axioms 2024, 13, 497.
• [11] D. Motreanu, E. Tornatore, Elliptic equations with unbounded coefficient, convection term and intrinsic operator, Math. Z. 308 (2024), no. 2, Paper no. 38.
• [12] D. Motreanu, C. Vetro, F. Vetro, The effects of convolution and gradient dependence on a parametric Dirichlet problem, Partial Differ. Equ. Appl. 1 (2020), no. 1, Paper no. 3.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr POPUL/SP/0154/2024/02 w ramach programu "Społeczna odpowiedzialność nauki II" - moduł: Popularyzacja nauki (2025)