Results 1 to 10 of about 138,114 (286)
Stability of Non-Linear Dirichlet Problems with ϕ-Laplacian. [PDF]
Entropy (Basel), 2021 We study the stability and the solvability of a family of problems −(ϕ(x′))′=g(t,x,x′,u)+f* with Dirichlet boundary conditions, where ϕ, u, f* are allowed to vary as well.
Bełdziński M, Galewski M, Kossowski I.
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Singular elliptic problems with Dirichlet or mixed Dirichlet-Neumann non-homogeneous boundary conditions [PDF]
Opuscula Mathematica, 2022 Let \(\Omega\) be a \(C^{2}\) bounded domain in \(\mathbb{R}^{n}\) such that \(\partial\Omega=\Gamma_{1}\cup\Gamma_{2}\), where \(\Gamma_{1}\) and \(\Gamma_{2}\) are disjoint closed subsets of \(\partial\Omega\), and consider the problem\(-\Delta u=g ...
Tomas Godoy
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Remarks on Nonlocal Dirichlet Problems
Mathematics, 2022 We study a nonlocal Dirichlet problem with the (p(b(u)),q(b(u)))-Laplacian operator and integrable data on a bounded domain with smooth boundary. We establish the existence of at least one weak solution in the case the variable exponents of the leading ...
Kholoud Saad Albalawi +2 more
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Parametric singular double phase Dirichlet problems
Advances in Nonlinear Analysis, 2023 We consider a parametric (with two parameters μ,λ>0\mu ,\lambda \gt 0) Dirichlet problem driven by the double phase differential operator and a reaction which has the competing effect of a singular term and of a superlinear perturbation.
Bai Yunru +2 more
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Dirichlet duality and the nonlinear Dirichlet problem [PDF]
Communications on Pure and Applied Mathematics, 2008 AbstractWe study the Dirichlet problem for fully nonlinear, degenerate elliptic equations of the form F(Hess u) = 0 on a smoothly bounded domain Ω ⋐ ℝn. In our approach the equation is replaced by a subset F ⊂ Sym2(ℝn) of the symmetric n × n matrices with ∂F ⊆ {F = 0}.
Harvey, F. Reese, Lawson, H. Blaine jun.
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Nonlinear Analysis, 2020 In this paper, optimal control problems containing ordinary nonlinear control systems described by fractional Dirichlet and Dirichlet–Neumann Laplace operators and a nonlinear integral performance index are studied. Using smooth-convex maximum principle,
Rafał Kamocki
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Strong solutions for singular Dirichlet elliptic problems
Electronic Journal of Qualitative Theory of Differential Equations, 2022 We prove an existence result for strong solutions $u\in W^{2,q}\left(\Omega\right) $ of singular semilinear elliptic problems of the form $-\Delta u=g\left( \cdot,u\right) $ in $\Omega,$ $u=\tau$ on $\partial\Omega,$ where ...
Tomas Godoy
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The problem of Dirichlet for an ellipsoid [PDF]
Terrestrial Magnetism and Atmospheric Electricity, 1935 (1) Introduction—In a group of important problems in potential theory it is required to determine a harmonic function which takes on preassigned continuous values on the boundaries of some region R. Under the proper limitations on the geometrical characteristics of the region R, it is known that the solution of the problem of Dirichlet exists and is ...
Sokolnikoff, I. S., Sokolnikoff, E. S.
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Dirichlet problems with unbalanced growth and convection
Electronic Journal of Qualitative Theory of Differential Equations, 2022 We consider a double phase Dirichlet problem with a gradient dependent reaction term (convection). Using the theory of nonlinear operators of monotone type, we show the existence of a bounded strictly positive solution.
Zhenhai Liu, Nikolaos Papageorgiou
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Nonlinear Eigenvalue Problems for the Dirichlet (p,2)-Laplacian
Axioms, 2022 We consider a nonlinear eigenvalue problem driven by the Dirichlet (p,2)-Laplacian. The parametric reaction is a Carathéodory function which exhibits (p−1)-sublinear growth as x→+∞ and as x→0+.
Yunru Bai +2 more
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