Results 61 to 70 of about 92,595 (298)
A Priori Bounds And Existence Of Positive Solutions For Semilinear Elliptic Systems [PDF]
, 2017 We provide a-priori L∞ bounds for classical positive solutions of semilinear elliptic systems in bounded convex domains when the nonlinearities are below the power functions v^p and u^q for any (p,q) lying on the critical Sobolev hyperbola.
Mavinga, Nsoki, Pardo, R.
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SEMILINEAR ELLIPTIC EQUATIONS IN UNBOUNDED SYMMETRIC DOMAINS
Taiwanese Journal of Mathematics, 1997 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tzeng, Shyuh-yaur, Wang, Hwai-chiuan
openaire +2 more sources
Weak solutions for a singular beam equation
ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Volume 105, Issue 12, December 2025.Abstract This paper deals with a dynamic Gao beam of infinite length subjected to a moving concentrated Dirac mass. Under appropriate regularity assumptions on the initial data, the problem possesses a weak solution which is obtained as the limit of a sequence of solutions of regularized problems.
Olena Atlasiuk +2 more
wiley +1 more source
On singular elliptic equations with measure sources [PDF]
, 2016 We prove existence of solutions for a class of singular elliptic problems with a general measure as source term whose model is $$\begin{cases} -\Delta u = \frac{f(x)}{u^{\gamma}} +\mu & \text{in}\ \Omega, u=0 &\text{on}\ \partial\Omega, u>0 &\text{on}\
Oliva, Francescantonio +1 more
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Mathematical Methods in the Applied Sciences, Volume 48, Issue 16, Page 14890-14908, 15 November 2025.ABSTRACT We analyze nonlinear degenerate coupled partial differential equation (PDE)‐PDE and PDE‐ordinary differential equation (ODE) systems that arise, for example, in the modelling of biofilm growth. One of the equations, describing the evolution of a biomass density, exhibits degenerate and singular diffusion.
K. Mitra, S. Sonner
wiley +1 more source
, 2011 In this paper, we prove that there exists a unique solution to the Dirichlet boundary value problem for a general class of semilinear second order elliptic partial differential equations. Our approach is probabilistic.
Zhang, Tusheng
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On semilinear elliptic equations with diffuse measures [PDF]
Nonlinear Differential Equations and Applications NoDEA, 2018 We consider semilinear equation of the form $$-Lu=f(x,u)+\mu $$-Lu=f(x,u)+μ, where L is the operator corresponding to a transient symmetric regular Dirichlet form $${\mathcal {E}}$$E, $$\mu $$μ is a diffuse measure with respect to the capacity associated
Tomasz Klimsiak, A. Rozkosz
semanticscholar +1 more source
Existence of Weak Solutions for a Degenerate Goursat‐Type Linear Problem
Mathematical Methods in the Applied Sciences, Volume 48, Issue 15, Page 14334-14341, October 2025.ABSTRACT For a generalization of the Gellerstedt operator with mixed‐type Dirichlet boundary conditions to a suitable Tricomi domain, we prove the existence and uniqueness of weak solutions of the linear problem and for a generalization of this problem.
Olimpio Hiroshi Miyagaki +2 more
wiley +1 more source
Multiple solutions of nonlinear partial functional differential equations and systems
Electronic Journal of Qualitative Theory of Differential Equations, 2019 We shall consider weak solutions of initial-boundary value problems for semilinear and nonlinear parabolic differential equations with certain nonlocal terms, further, systems of elliptic functional differential equations.
László Simon
doaj +1 more source
Construction of blow‐up solutions for Liouville systems
Proceedings of the London Mathematical Society, Volume 131, Issue 4, October 2025.Abstract We study the following Liouville system defined on a flat torus −Δui=∑j=1naijρjhjeuj∫Ωhjeuj−1,uj∈Hper1(Ω)fori∈I={1,…,n},$$\begin{equation*} {\left\lbrace \def\eqcellsep{&}\begin{array}{lr}-\Delta u_i=\sum _{j=1}^n a_{ij}\rho _j{\left(\frac{h_j e^{u_j}}{\int _\Omega h_j e^{u_j}}-1\right)},\\[3pt] u_j\in H_{per}^1(\Omega)\mbox{ for }i\in I ...
Zetao Cheng, Haoyu Li, Lei Zhang
wiley +1 more source