Results 61 to 70 of about 232 (181)
Smooth subsolutions of the discounted Hamilton-Jacobi equations
Differential and Integral EquationsFor the discounted Hamilton-Jacobi equation,$$λu+H(x,d_x u)=0, \ x \in M, $$we construct $C^{1,1}$ subsolutions which are indeed solutions on the projected Aubry set. The smoothness of such subsolutions can be improved under additional hyperbolicity assumptions.
Huang, Xiyao +3 more
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Six One‐Sign Solutions for Semilinear Elliptic Problems in ℝN*
Journal of Function Spaces, Volume 2026, Issue 1, 2026.In this work, we consider the existence of one‐sign solutions for semilinear elliptic problems: {−Δu = λa(x)f(u), in ℝN, u(x)⟶0, as|x|⟶+∞, where N ≥ 3, λ is a real parameter and a ∈ C(ℝN, ℝ) is a weighted function, f ∈ C(ℝ, ℝ). Furthermore, by bifurcation technique, we identify the interval of bifurcation parameter in which the semilinear elliptic ...
Wenguo Shen, Claudia Capone
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Mean values of subsolutions of elliptic and parabolic equations [PDF]
Transactions of the American Mathematical Society, 1983 Integral averages of weak subsolutions (and supersolutions) in R n
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Journal of Mathematics, Volume 2026, Issue 1, 2026.Inspired by a fundamental existence result in the theory of PDEs, we present a general existence theorem for viscosity solutions in the standard sense that is applicable to a wide class of partial differential equations. These equations are characterized by coefficients that are merely measurable, with no continuity assumptions imposed.
S. M. E. Hosseini +2 more
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Subsolutions and supersolutions in a free boundary problem
Arkiv för Matematik, 1994 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On uniqueness of solutions to complex Monge–Ampère mean field equations
Bulletin of the London Mathematical Society, Volume 57, Issue 10, Page 3163-3180, October 2025.Abstract We establish the uniqueness of solutions to complex Monge–Ampère mean field equations when (minus) the temperature parameter is small. In the local setting of bounded hyperconvex domains, our result partially confirms a conjecture by Berman and Berndtsson. Our approach also extends to the global context of compact complex manifolds.
Chinh H. Lu, Trong‐Thuc Phung
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Positive evanescent solutions of singular elliptic problems in exterior domains
Electronic Journal of Qualitative Theory of Differential Equations, 2016 We investigate the existence of positive solutions for the following class of nonlinear elliptic problems \[\operatorname{div}(a(\|x\|)\nabla u(x))+f(x,u(x))-(u(x))^{-\alpha}\|\nabla u(x)\|^{\beta}+g(\|x\|)x\cdot\nabla u(x)=0,\] where $x\in\mathbb{R}^{n}$
Aleksandra Orpel
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The robust Orlicz risk with an application to the green photovoltaic power generation
Asian Journal of Control, Volume 27, Issue 4, Page 1655-1667, July 2025.Abstract We propose a novel recursive utility for controlling stochastic processes under risk and uncertainty. Our formulation uses a robustified Orlicz risk that can evaluate risk and uncertainty simultaneously. We focus on the control problem of a photovoltaic power generation system that supplies excess electricity for the secondary purpose of ...
Hidekazu Yoshioka, Motoh Tsujimura
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Asymptotic behavior of positive solutions of a semilinear Dirichlet problem outside the unit ball
Electronic Journal of Differential Equations, 2013 In this article, we are concerned with the existence, uniqueness and asymptotic behavior of a positive classical solution to the semilinear boundary-value problem $$displaylines{ -Delta u=a(x)u^{sigma }quadext{in }D, cr lim _{|x|o 1}u(x)= lim_{|x|o ...
Habib Maagli +2 more
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Positive symmetric solutions of singular semipositone boundary value problems
Electronic Journal of Qualitative Theory of Differential Equations, 2009 Using the method of upper and lower solutions, we prove that the singular boundary value problem, \[ -u'' = f(u) ~ u^{-\alpha} \quad \textrm{in} \quad (0, 1), \quad u'(0) = 0 = u(1) \, , \] has a positive solution when $0 < \alpha < 1$ and $f : \mathbb ...
M. Rudd, Christopher Tisdell
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