Nonlocal Kirchhoff Problems with Singular Exponential Nonlinearity
نویسندگان
چکیده
منابع مشابه
The singular extremal solutions of the bilaplacian with exponential nonlinearity
Consider the problem ∆u = λe in B u = ∂u ∂n = 0 on ∂B, where B is the unit ball in R and λ is a parameter. Unlike the Gelfand problem the natural candidate u = −4 ln(|x|), for the extremal solution, does not satisfy the boundary conditions and hence showing the singular nature of the extremal solution in large dimensions close to the critical dimension is challenging. Dávila et al. in [5] use...
متن کاملBifurcation and Asymptotics for Elliptic Problems with Singular Nonlinearity
We report on some recent existence and uniqueness results for elliptic equations subject to Dirichlet boundary condition and involving a singular nonlinearity. We take into account the following types of problems: (i) singular problems with sublinear nonlinearity and two parameters; (ii) combined effects of asymptotically linear and singular nonlinearities in bifurcation problems; (iii) bifurca...
متن کاملA Diffusion Equation with Exponential Nonlinearity Recant Developments
The purpose of this paper is to analyze in detail a special nonlinear partial differential equation (nPDE) of the second order which is important in physical, chemical and technical applications. The present nPDE describes nonlinear diffusion and is of interest in several parts of physics, chemistry and engineering problems alike. Since nature is not linear intrinsically the nonlinear case is t...
متن کاملSingular limits for reaction-diffusion equations with fractional Laplacian and local or nonlocal nonlinearity
We perform an asymptotic analysis of models of population dynamics with a fractional Laplacian and local or nonlocal reaction terms. The first part of the paper is devoted to the long time/long range rescaling of the fractional Fisher-KPP equation. This rescaling is based on the exponential speed of propagation of the population. In particular we show that the only role of the fractional Laplac...
متن کاملDispersive shock waves with nonlocal nonlinearity.
We consider dispersive optical shock waves in nonlocal nonlinear media. Experiments are performed using spatial beams in a thermal liquid cell, and results agree with a hydrodynamic theory of propagation.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Applied Mathematics & Optimization
سال: 2020
ISSN: 0095-4616,1432-0606
DOI: 10.1007/s00245-020-09666-3