相关论文: Infinitely many symmetric solutions for anisotropi…
We investigate the effect of non-symmetric relatively bounded perturbations on the spectrum of self-adjoint operators. In particular, we establish stability theorems for one or infinitely many spectral gaps along with corresponding…
By means of topological methods, we provide new results on the existence, non-existence, localization and multiplicity of nontrivial solutions for systems of perturbed Hammerstein integral equations. In order to illustrate our theoretical…
We investigate the existence of least energy solutions and infinitely many solutions for the following nonlinear fractional equation (-\Delta)^{s} u = g(u) \mbox{ in } \mathbb{R}^{N}, where $s\in (0,1)$, $N\geq 2$, $(-\Delta)^{s}$ is the…
A non-homogeneous conormal derivative problem is considered for quasilinear divergence form elliptic equations modeled on the $m$-Laplacian operator. The nonlinear terms are given by Carath\'eodory functions and satisfy controlled growth…
This paper is devoted to prove the existence of one or multiple solutions of a wide range of nonlinear differential boundary value problems. To this end, we obtain some new fixed point theorems for a class of integral operators. We follow…
By employing supersymmetric quantum mechanics, we present a general algorithm to construct supersymmetric partner potentials and hence derive exact stationary solutions of the inhomogeneous nonlinear Schr\"odinger equation (INLSE). This is…
We study a boundary-value quasilinear elliptic problem on a generic time scale. Making use of the fixed-point index theory, sufficient conditions are given to obtain existence, multiplicity, and infinite solvability of positive solutions.
It is shown by means of reiterated two-scale convergence in the Sobolev-Orlicz setting, that the sequence of solutions of a class of highly oscillatory problems involving nonlinear elliptic operators with nonstandard growth, converges to a…
An iterative learning algorithm is presented for continuous-time linear-quadratic optimal control problems where the system is externally symmetric with unknown dynamics. Both finite-horizon and infinite-horizon problems are considered. It…
We clarify how close a second order fully nonlinear equation can come to uniform ellipticity, through counting large eigenvalues of the linearized operator. This suggests an effective and novel way to understand the structure of fully…
In this paper we consider some non-stationary relaxed synchronous and asynchronous multi-splitting methods for solving the linear complementarity problems with their coefficient matrices being H-matrices. The convergence theorems of the…
Multilinear systems of equations arise in various applications, such as numerical partial differential equations, data mining, and tensor complementarity problems. In this paper, we propose a homotopy method for finding the unique positive…
We construct multibump nodal solutions of the elliptic equation $$ -\Delta u=a^+[\lambda u+ f(\, \cdot\,, u)]-\mu a^- g(\, \cdot\,, u) $$ in $H^1_0(\Omega)$, when $\mu$ is large, under appropriate assumptions, for $f$ superlinear and…
Under quasi-monotone assumptions for coefficients, we show one kind of comparison theorem for multi-dimensional\textbf{\}backward doubly stochastic differential equations on infinite horizon. An example is given as well.
We consider finite-dimensional nonlinear systems with linear part described by a parity-time (PT-) symmetric operator. We investigate bifurcations of stationary nonlinear modes from the eigenstates of the linear operator and consider a…
We investigate the existence and uniqueness of solutions for second-order semi-linear partial differential equations defined on a Riemannian manifold $M$. By combining differential geometry and analysis techniques, we establish the…
We study parameterized elliptic systems on symmetric domains with additional system symmetries. We prove the existence of continua of nontrivial solutions bifurcating from the constant branch determined by a critical point of the potential,…
We provide new results on the existence, non-existence and multiplicity of non-negative radial solutions for semilinear elliptic systems with Neumann boundary conditions on an annulus. Our approach is topological and relies on the classical…
We review recent progress in the study of infinite-dimensional stochastic differential equations with symmetry. This paper contains examples arising from random matrix theory.
We lift the constraint of a diagonal representation of the Hamiltonian by searching for square integrable bases that support a tridiagonal matrix representation of the wave operator. Doing so results in exactly solvable problems with a…