Related papers: Ground state solutions for the nonlinear Klein-Gor…
This paper deals with the Klein-Gordon-Maxwell system in a bounded spatial domain. We study the existence of solutions having a specific form, namely standing waves in equilibrium with a purely electrostatic field. We prescribe Dirichlet…
In this paper, we study a class of quasilinear elliptic equations which appears in nonlinear optics. By using the mountain pass theorem together with a technique of adding one dimension of space, we prove the existence of a non-trivial weak…
We study the existence of ground states to a nonlinear fractional Kirchhoff equation with an external potential $V$. Under suitable assumptions on $V$, using the monotonicity trick and the profile decomposition, we prove the existence of…
This paper is concerned with the Klein-Gordon-Maxwell system in a bounded spatial domain. We discuss the existence of standing waves $\psi=u(x)e^{-i\omega t}$ in equilibrium with a purely electrostatic field $\mathbf{E}=-\nabla\phi(x)$. We…
We prove the existence of positive solutions to a sys- tem of k non-linear elliptic equations corresponding to standing- wave k-uples solutions to a system of non-linear Klein-Gordon equations. Our solutions are characterised by a small…
We prove the existence of radial and radially decreasing ground states of an m-coupled nonlinear Schrodinger equation with a general nonlinearity.
We extend our previous result on the focusing cubic Klein-Gordon equation in three dimensions to the non-radial case, giving a complete classification of global dynamics of all solutions with energy at most slightly above that of the ground…
We introduce mountain-pass type arguments in the context of orbital instability for Klein-Gordon equations. Our aim is to illustrate on two examples how these arguments can be useful to simplify proofs and derive new results of orbital…
We study a Klein-Gordon-Maxwell system, in a bounded spatial domain, under Neumann boundary conditions on the electric potential. We allow a nonconstant coupling coefficient. For sufficiently small data, we find infinitely many static…
We look for three dimensional vortex-solutions, which have finite energy and are stationary solutions, of Klein-Gordon-Maxwell-Proca type systems of equations. We prove the existence of three dimensional cylindrically symmetric…
In this paper we prove the existence of positive ground state solution for a class of linearly coupled systems involving Kirchhoff-Schr\"odinger equations. We study the subcritical and critical case. Our approach is variational and based on…
We study the existence of ground and bound state solutions for a system of coupled Schr\"odinger equations with linear and nonlinear couplings in $\mathbb{R}^N$. By studying the limit system and using concentration compactness arguments, we…
The existence of ground states and (multiple) bound states to semilinear time-independent Maxwell and Schr\"odinger equations, with or without $L^2$-constraints, is investigated.
The paper studies existence of ground states for the nonlinear Schr\"odinger equation with a general external magnetic field. In particular, no lattice periodicity or symmetry of the magnetic field, or presence of external electric field is…
We solve the Klein-Gordon equation in the presence of a spatially one-dimensional cusp potential. The bound state solutions are derived and the antiparticle bound state is discussed.
We prove the existence of a ground state and infinitely many geometrically distinct solutions for static nonlinear Maxwell's equations on $\mathbb{R}^3$. Our existence result relies on a variant of the Symmetric Mountain Pass Theorem that…
In this paper we prove existence of ground state solutions of the modified nonlinear Schrodinger equation: $$ -\Delta u+V(x)u-{1/2}u \Delta u^{2}=|u|^{p-1}u, x \in \R^N, N \geq 3, $$ under some hypotheses on $V(x)$. This model has been…
In the paper we present a functional-discrete method for solving the Goursat problem for nonlinear Klein-Gordon equation. The sufficient conditions providing that the proposed method converges superexponentially are obtained. The results of…
In this paper we study existence and orbital stability for solitary waves of the nonlinear Klein-Gordon equation. The energy of these solutions travels as a localized packet, hence they are a particular type of solitons. In particular we…
We prove existence and uniform bounds for electrostatic Klein-Gordon-Maxwell systems in the inhomogeneous context of a compact Riemannian manifold when the mass potential, balanced by the phase, is small in a quantified sense.