Related papers: Solutions to a nonlinear Maxwell equation with two…
The Maxwell's equations are solved when it has an inhomogeneous terms as a source. The solution is very general in a sense that it handles arbitrary current source and anisotropic media. The calculation is carried out in the k-domain after…
We obtain a class of magnetically charged solutions in 2+1 dimensional Einstein - Power - Maxwell theory. In the linear Maxwell limit, such horizonless solutions are known to exist. We show that in 3D geometry, black hole solutions with…
We study solutions $(x_n)_{n \in \mathbb{N}}$ of nonhomogeneous nonlinear second order difference equations of the type $\ell_n = x_n ( \sigma_{n,1} x_{n+1} + \sigma_{n,0} x_n + \sigma_{n,-1} x_{n-1} ) + \kappa_n x_n$, with given initial…
The evolution of an electrically conducting imcompressible fluid with nonconstant density can be described by a set of equations combining the continuity, momentum and Maxwell's equations; altogether known as the inhomogeneous…
We study the Schr\"{o}dinger equation: \begin{eqnarray} - \Delta u+V(x)u+f(x,u)=0,\qquad u\in H^{1}(\mathbb{R}^{N}),\nonumber \end{eqnarray} where $V$ is periodic and $f$ is periodic in the $x$-variables, $0$ is in a gap of the spectrum of…
We prove that in contrast to the free wave equation in $\R^3$ there are no incoming solutions of Maxwell's equations in the form of spherical or modulated spherical waves. We construct solutions which are corrected by lower order incoming…
In this paper, we study the existence and multiplicity results of nontrivial positive solutions to a quasilinear elliptic equation in $\RN$, when $N\geq2$, as \begin{equation} \Lp…
In this paper, we consider the quasilinear Schr\"{o}dinger equation \begin{equation*} -\Delta u+V(x)u-u\Delta(u^2)=g(u),\ \ x\in \mathbb{R}^{3}, \end{equation*} where $V$ and $g$ are continuous functions. Without the coercive condition on…
In this paper we deal with positive solutions for singular quasilinear problems whose model is $$ \begin{cases} -\Delta u + \frac{|\nabla u|^2}{(1-u)^\gamma}=g & \mbox{in $\Omega$,}\newline \hfill u=0 \hfill & \mbox{on $\partial\Omega$,}…
The goal is a construction of stationary solutions close to a non-trivial combination of two plane waves at high energies for a periodic non-linear Schroedinger equation in dimension two. The corresponding isoenergetic surfaces are…
We study the existence of positive solutions of a particular elliptic system in $\mathbb{R}^3$ composed of two coupled non linear stationary Schr\"odinger equations (NLSEs), that is $-\epsilon^2 \Delta u + V(x) u= h_v(u,v), - \epsilon^2…
We prove existence and multiplicity results for finite energy solutions to the nonlinear elliptic equation \[ -\triangle u+V\left( \left| x\right| \right) u=g\left( \left| x\right| ,u\right) \quad \textrm{in }\Omega \subseteq…
We study the Landau-Lifshitz system associated with Maxwell equations in a bilayered ferromagnetic body when super-exchange and surface anisotropy interactions are present in the spacer in-between the layers. In the presence of these…
In this work we analyze the existence of solutions to the nonlinear elliptic system: \begin{equation*} \left\{ \begin{array}{rcll} -\Delta u & = & v^q+\a g & \text{in }\Omega , \\ -\Delta v& = &|\nabla u|^{p}+\l f &\text{in }\Omega , \\…
We have considered an expansion of solutions of the non-linear equations for both longitudinal and transverse waves in collisionless Maxwellian plasma in series of non-damping overtones of the field E(x,t) and electron velocity distribution…
We construct solutions to the nonlinear magnetic Schr\"odinger equation $$ \left\{ \begin{aligned} - \varepsilon^2 \Delta_{A/\varepsilon^2} u + V u &= \lvert u\rvert^{p-2} u & &\text{in}\ \Omega,\\ u &= 0 & &\text{on}\ \partial\Omega,…
The features of propagation of intense waves are of great interest for theory and experiment in electrodynamics and acoustics. The behavior of nonlinear waves in a bounded volume is of especial importance and, at the same time, is an…
The present paper studies the existence of weak solutions for the following type of non-homogeneous system of equations \begin{equation*} (S) \left\{\begin{aligned} (-\Delta)^{s_1}_{p_1} u &=u|u|^{\alpha-1}|v|^{\beta+1}+f_1(x) \,\mbox{ in…
The authors of this paper deal with the existence and regularities of weak solutions to the homogenous $\hbox{Dirichlet}$ boundary value problem for the equation $-\hbox{div}(|\nabla u|^{p-2}\nabla u)+|u|^{p-2}u=\frac{f(x)}{u^{\alpha}}$.…
We investigate a class of Kirchhoff type equations involving a combination of linear and superlinear terms as follows: \begin{equation*} -\left( a\int_{\mathbb{R}^{N}}|\nabla u|^{2}dx+1\right) \Delta u+\mu V(x)u=\lambda…