Related papers: On self-similar solutions of a multi-phase Stefan …
We investigate the existence of two nontrivial solutions for a poly-Laplacian system involving concave-convex nonlinearities and parameters with Dirichlet boundary condition on locally finite graphs. By using the mountain pass theorem and…
The aim of this paper is to prove the existence of multiple solutions for a family of nonlinear elliptic systems in divergence form coupled with a pointwise gradient constraint: \begin{align*} \left\{ \begin{array}{ll}…
On the contrary to the common intuition, which suggests that a steep expulsive potential makes quantum states widely delocalized, we demonstrate that one- and two-dimensional (1D and 2D) Schroedinger equations, which include expulsive…
In this article we study the structure of solutions to the one-phase Bernoulli problem that are modeled either infinitesimally or at infinity by one-homogeneous solutions with an isolated singularity. In particular, we prove a uniqueness of…
In this paper, we consider the following free boundary problem $$ (P)\left\{\begin{array}{ll} \Delta u = \lambda \phi(x)\Sum_{i=1}^n H(u-\mu_i )& \quad \mbox{ in }\ \Omega=\Omega_2\setminus \overline{\Omega}_1, \\[0.3cm]u =0 &\quad \mbox{…
This paper is concerned with the periodic (in time) solutions to an one-dimensional semilinear wave equation with $x$-dependent coefficient. Such a model arises from the forced vibrations of a nonhomogeneous string and propagation of…
In this paper we study one dimensional parabolic free boundary value problem with a nonlocal (integro-differential) condition on the free boundary. We establish global existence-uniqueness of classical solutions assuming that the…
In this paper, we mainly establish the existence of at least three non-trivial solutions for a class of nonhomogeneous quasilinear elliptic systems with Dirichlet boundary value or Neumann boundary value in a bounded domain…
In the present work, we consider existence and multiplicity of positive solutions for nonlocal elliptic problems driven by the Stein-Weiss problem with concave-convex nonlinearities defined in the whole space $\mathbb{R}^N$. More precisely,…
In the present paper, we study a singular double phase variable exponent Dirichlet problem in the setting of a new Musielak-Orlicz Sobolev space with the nonlinearity (the external source) having gradient dependence (so-called convection…
We consider the problem of maximizing a convex function over a closed convex set in a real Hilbert space. For linear functions, we show that a single orthogonal projection suffices to obtain an approximate solution. For continuous convex…
Solving Stefan problems via neural networks is inherently challenged by the nonlinear coupling between the solutions and the free boundary, which results in a non-convex optimization problem. To address this, this work proposes an Operator…
We study a class of nonlinear elliptic problems driven by a double-phase operator with variable exponents, arising in the modeling of heterogeneous materials undergoing phase transitions. The associated Poisson problem features a…
Topology optimization of frame structures under free-vibration eigenvalue constraints constitutes a challenging nonconvex polynomial optimization problem with disconnected feasible sets. In this article, we first formulate it as a…
In this paper we extend the classical sub-supersolution Sattinger iteration method to $1$-Laplace type boundary value problems of the form \begin{equation*} \begin{cases} \displaystyle -\Delta_1 u = F(x,u) & \text{in}\;\Omega,\\ \newline…
A nonlocal nonlinear Schr\"odinger equation with focusing nonlinearity is considered which has been derived as a continuum limit of the Calogero-Sutherland model in an integrable classical dynamical system. The equation is shown to stem…
In this paper we consider a one-dimensional one-phase Stefan problem corresponding to the solidification process of a semi-infinite material with a convective boundary condition at the fixed face. The exact solution of this problem,…
For minimizing a strongly convex objective function subject to linear inequality constraints, we consider a penalty approach that allows one to utilize stochastic methods for problems with a large number of constraints and/or objective…
In this paper we derive an obstacle problem with a free boundary to describe the formation of voids at areas of intense geological folding. An elastic layer is forced by overburden pressure against a V-shaped rigid obstacle. Energy…
A thermodynamically consistent two-phase Stefan problem with temperature-dependent surface tension and with or without kinetic undercooling is studied. It is shown that these problems generate local semiflows in well-defined state…