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The main concern of this paper is to mathematically investigate the formation of a plasma sheath near the surface of nonplanar walls. We study the existence and asymptotic stability of stationary solutions for the nonisentropic…
Using some nonlinear domain decomposition method, we prove the existence of singular limits for solution of semilinear elliptic problems with exponential nonlinearity.
A generalization of the Euler's elastic problem, i.e., finding a stationary configuration (planar elastica) of the Bernoulli's thin ideal elastic rod with boundary conditions defined through fixed endpoints and/or tangents at the endpoints,…
We prove the existence and uniqueness of solution of quasilinear stochastic partial differential equations with obstacle (OSPDEs in short) in degenerate case. Using De Giorgi's iteration, we deduce the $L^p-$estimates for the time-space…
A new method to solve computationally challenging (random) parametric obstacle problems is developed and analyzed, where the parameters can influence the related partial differential equation (PDE) and determine the position and surface…
Fractional-order elliptic problems are investigated in case of inhomogeneous Dirichlet boundary data. The boundary integral form is proposed as a suitable mathematical model. The corresponding theory is completed by sharpening the mapping…
In this work, we shall consider the existence and uniqueness of stationary solutions to stochastic partial functional differential equations with additive noise in which a neutral type of delay is explicitly presented. We are especially…
Ground state solutions of elliptic problems have been analyzed extensively in the theory of partial differential equations, as they represent fundamental spatial patterns in many model equations. While the results for scalar equations, as…
This work is devoted to the study of the existence of at least one weak solution to nonlocal equations involving a general integro-differential operator of fractional type. As a special case, we derive an existence theorem for the…
Motivated by the existing complications of finding solutions of Eringen nonlocal model, an alternative model is developed here. The new formulation of the nonlocal elasticity is centered upon expressing the dynamic equilibrium requirements…
We solve elliptic systems of equations posed on highly heterogeneous materials. Examples of this class of problems are composite structures and geological processes. We focus on a model problem which is a second-order elliptic equation with…
Some systems of parabolic equations with nonlocal initial conditions are studied. The systems arise when considering steady-state solutions to diffusive age-structured cooperative or competing species. Local and global bifurcation…
This paper examines impulsive non-autonomous systems with grazing periodic solutions. Surfaces of discontinuity and impact functions of the systems are not depending on the time variable. That is, we can say that the impact conditions are…
We introduce variational problems on Riemannian manifolds with constrained acceleration and derive necessary conditions for normal extremals in the constrained variational problem. The problem consists on minimizing a higher-order energy…
We investigate the small-time local controllability (STLC) near the ground state of a bilinear Schr\"odinger equation when the linearized system is not controllable. It is well known that, for single-input systems, quadratic terms in the…
We consider positive solutions to semilinear elliptic problems with singular nonlinearities, under zero Dirichlet boundary condition. We exploit a refined version of the moving plane method to prove symmetry and monotonicity properties of…
This paper studies the existence of multiple non-trivial stationary solutions of a partial differential equation (PDE) model introduced in [3], motivated by collective ant behavior. Previous work suggested the presence of two types of…
For the stationary nonlinear Schr\"odinger equation $-\Delta u+ V(x)u- f(u) = \lambda u$ with periodic potential $V$ we study the existence and stability properties of multibump solutions with prescribed $L^2$-norm. To this end we introduce…
In this work, we shall investigate existence and multiplicity of solutions for a nonlocal elliptic systems driven by the fractional Laplacian. Specifically, we establish the existence of two positive solutions for following class of…
Existence of stationary point vortices solution to the damped and stochastically driven Euler's equation on the two dimensional torus is proved, by taking limits of solutions with finitely many vortices. A central limit scaling is used to…