Results 41 to 50 of about 1,290,485 (220)
Inverse problems for semilinear elliptic PDE with a general nonlinearity a(x,u)$a(x,u)$
Transactions of the London Mathematical Society, Volume 13, Issue 1, December 2026.Abstract This article studies the inverse problem of recovering a nonlinearity in an elliptic equation Δu+a(x,u)=0$\Delta u + a(x,u) = 0$ from boundary measurements of solutions. Previous results based on first‐order linearization achieve this under a sign condition on ∂ua(x,u)$\partial _u a(x,u)$, and results based on higher order linearization ...
David Johansson +2 more
wiley +1 more source
Quantitative maximal L2$L^2$‐regularity for viscous Hamilton–Jacobi PDEs in 2D and Mean Field Games
Bulletin of the London Mathematical Society, Volume 58, Issue 11, November 2026.Abstract We discuss quantitative Calderón–Zygmund estimates in W2,2$W^{2,2}$ for 2D viscous Hamilton–Jacobi equations with natural growth in the gradient. We apply the result to obtain the existence of classical solutions for stationary second‐order mean field games systems in 2D with (defocusing) coupling behaving like mα$m^\alpha$ for any α>0$\alpha >
Alessandro Goffi
wiley +1 more source
Semilinear elliptic equations with dependence on the gradient via Mountain-Pass techniques [PDF]
, 2004 A class of semilinear elliptic equations with dependence on the gradient is considered. The existence of a positive and a negative solution is stated through an iterative method based on Mountain Pass ...
Matzeu, M +6 more
core +1 more source
Existencia de Soluciones Radiales para Problemas Semilineales Elípticos Indefinidos
Selecciones Matemáticas, 2020 We study the existence of radial solutions of indefinite semilinear elliptic equations in the unit ball in Rn (n>=3) with Dirichlet boundary conditions, whose nonlinear term has the form lamda.m(|x|)f(u) where m(|.|) is radially symmetric, discontinuous ...
Marco Calahorrano, Israel Cevallos
doaj +1 more source
Numerical Methods for Partial Differential Equations, Volume 42, Issue 5, September 2026.ABSTRACT In this work, we present an extension of the semi‐discrete Lagrangian‐Eulerian numerical scheme for diffusive‐dispersive conservation law problems, including a jump discontinuous flux function. As in the one‐dimensional scalar hyperbolic case, the no‐flow curves also organize the geometry of the method.
Eduardo Abreu +2 more
wiley +1 more source
Existence and Multiplicity of Solutions of Semilinear Elliptic Equations
Journal of Mathematical Analysis and Applications, 2001 The paper deals with the semilinear elliptic Dirichlet boundary problem \[ \begin{cases} -\Delta u=f(x,u)\quad & \text{in }\Omega,\\ u=0\quad &\text{on } \partial \Omega,\end{cases} \tag{1} \] where \(\Omega\subset R^d\) \((d\geq 1)\) is a bounded smooth domain and \(f:\overline\Omega\times R\to R\) is a Carathéodory function. Throughout this paper the
Tang, Chun-Lei, Wu, Xing-Ping
openaire +1 more source
L∞$L^\infty$ compactness of solutions of quasilinear problems and applications
Journal of the London Mathematical Society, Volume 114, Issue 3, September 2026.Abstract For a (not necessarily smooth) bounded domain Ω$\Omega$ of RN$\mathbb {R}^N$, N⩾2$N \geqslant 2$ and a Carathéodory vector‐valued function a:Ω×RN→RN$a:\Omega \times \mathbb {R}^N \rightarrow \mathbb {R}^N$, we study the compactness of the inverse of the Leray–Lions operator A(u)=−div(a(x,∇u))$A(u)=-\text{div}(a(x, \nabla u))$, u∈W01,p(Ω)$u\in ...
D. Arcoya +2 more
wiley +1 more source
Electronic Journal of Differential Equations, 2000 solutions to nonlinear equations and to (non)resonant semilinear equations involving nonlinear perturbations of Fredholm maps of index zero. We apply our results to semilinear elliptic, and to semilinear parabolic and hyperbolic periodic boundary-value ...
P. S. Milojevic
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Well‐Posedness and Analyticity of Solutions to the Stationary MHD Equations
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Volume 106, Issue 8, August 2026.ABSTRACT We consider the stationary problem of the MHD equations in R3$\mathbb {R}^3$. The aim of this article is to show existence, uniqueness, regularity, and analyticity of solutions in the scaling invariant homogeneous Besov space Ḃp,q−1+3/p$\dot{B}^{-1 + 3/p}_{p, q}$ for 1⩽p<3$1 \leqslant p < 3$ and 1⩽q⩽∞$1 \leqslant q \leqslant \infty$.
Kento Sube
wiley +1 more source
Existence of solutions of the Dirichlet problem for an infinite system of nonlinear differential-functional equations of elliptic type [PDF]
Opuscula Mathematica, 2005 The Dirichlet problem for an infinite weakly coupled system of semilinear differential-functional equations of elliptic type is considered. It is shown the existence of solutions to this problem.
Tomasz S. Zabawa
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