Results 1 to 10 of about 137,065 (288)
Stability of Non-Linear Dirichlet Problems with ϕ-Laplacian [PDF]
Entropy, 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.
Michał Bełdziński +2 more
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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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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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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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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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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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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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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 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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The Dirichlet Casimir problem [PDF]
Nuclear Physics B, 2004 Casimir forces are conventionally computed by analyzing the effects of boundary conditions on a fluctuating quantum field. Although this analysis provides a clean and calculationally tractable idealization, it does not always accurately capture the characteristics of real materials, which cannot constrain the modes of the fluctuating field at all ...
Graham, N. +5 more
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