Results 71 to 80 of about 511,067 (272)

A New Extended Jacobi Elliptic Function Expansion Method and Its Application to the Generalized Shallow Water Wave Equation

Journal of Applied Mathematics, 2012
With the aid of symbolic computation, a new extended Jacobi elliptic function expansion method is presented by means of a new ansatz, in which periodic solutions of nonlinear evolution equations, which can be expressed as a finite Laurent series of some ...
Yafeng Xiao, Haili Xue, Hongqing Zhang
doaj   +1 more source

Boundary Value Problems for Mixed Type Equations and Applications

, 2011
In this paper we outline a general method for finding well-posed boundary value problems for linear equations of mixed elliptic and hyperbolic type, which extends previous techniques of Berezanskii, Didenko, and Friedrichs.
Khuri, Marcus A.
core   +1 more source

Finite Morse index solutions and asymptotics of weighted nonlinear elliptic equations [PDF]

Advances in Differential Equations, 2013
By introducing a suitable setting, we study the behavior of finite Morse index solutions of the equation \[ -\{div} (|x|^\theta \nabla v)=|x|^l |v|^{p-1}v \;\;\; \{in $\Omega \subset \R^N \; (N \geq 2)$}, \leqno(1) \] where $p>1$, $\theta, l\in\R^1 ...
Yihong Du, Zongming Guo
semanticscholar   +1 more source

Regularity for solutions to nonlinear elliptic equations

Differential and Integral Equations, 2013
Let $\Omega$ be a domain of ${\mathbb R}^N$, $N>2.$ We establish higher integrability for solutions $u \in W^{1,p}_{\text{loc}}(\Omega)$ of nonlinear PDEs whose prototype~is \begin{equation*} \text{div\,}[|\nabla u|^{p-2}\nabla u +B(x)|u|^{p-2}u]=\text{div\,}(|F|^{p-2}F) \end{equation*} with $1 < p < N$.
GRECO, LUIGI, MOSCARIELLO, GIOCONDA, ZECCA, GABRIELLA   +2 more
openaire   +3 more sources

Nonparaxial elliptic waves and solitary waves in coupled nonlinear Helmholtz equations

, 2015
We obtain a class of elliptic wave solutions of coupled nonlinear Helmholtz (CNLH) equations describing nonparaxial ultra-broad beam propagation in nonlinear Kerr-like media, in terms of the Jacobi elliptic functions and also discuss their limiting forms
Kanna, T., Khare, Avinash, Tamilselvan, K.   +2 more
core   +1 more source

Nonlinear Elliptic Equations with Singular Terms and Combined Nonlinearities [PDF]

Annales Henri Poincaré, 2011
We consider nonlinear elliptic Dirichlet problems with a singular term, a concave (i.e., (p − 1)-sublinear) term and a Caratheodory perturbation. We study the cases where the Caratheodory perturbation is (p − 1)-linear and (p − 1)-superlinear near +∞. Using variational techniques based on the critical point theory together with truncation arguments and
Gasiński, Leszek, Papageorgiou, Nikolaos S.   +1 more
openaire   +3 more sources

survey on boundary regularity for the fractional p-Laplacian and its applications

Bruno Pini Mathematical Analysis Seminar
We survey some recent regularity results for fractional p-Laplacian elliptic equations, especially focusing on pure and weighted boundary Hölder continuity of the solutions of related Dirichlet problems. Then, we present some applications of such results
Antonio Iannizzotto
doaj   +1 more source

Maximum principles for viscosity solutions of weakly elliptic equations

Bruno Pini Mathematical Analysis Seminar, 2019
Maximum principles play an important role in the theory of elliptic equations. In the last decades there have been many contributions related to the development of fully nonlinear equations and viscosity solutions.
Antonio Vitolo
doaj   +1 more source

Positive solutions of nonlinear elliptic equations

Applied Mathematics Letters, 2008
AbstractThis work deals with the existence of positive solutions of convection–diffusion equations Δu+f(x,u,∇u)=0 in an exterior domain of Rn(n≥3).
Wang, S.P., Yeh, C.C., Wong, F.H.
openaire   +3 more sources

Continuous dependence estimates for viscosity solutions of fully nonlinear degenerate elliptic equations

Electronic Journal of Differential Equations, 2002
Using the maximum principle for semicontinuous functions [3,4], we prove a general ``continuous dependence on the nonlinearities'' estimate for bounded Holder continuous viscosity solutions of fully nonlinear degenerate elliptic equations.
Espen R. Jakobsen, Kenneth H. Karlsen
doaj