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In this article, we focus on a doubly nonlinear nonlocal parabolic initial boundary value problem driven by the fractional $p$-Laplacian equipped with homogeneous Dirichlet boundary conditions on a domain in $\mathbb{R}^{d}$ and composed…

Numerical solution of the Poisson equation in metallic enclosures, open at one or more ends, is important in many practical situations such as High Power Microwave (HPM) or photo-cathode devices. It requires imposition of a suitable…

In a multidimensional infinite layer bounded by two hyperplanes, the inhomogeneous Helmholtz equation with a polynomial right-hand side is considered. It is shown that the Dirichlet and Dirichlet-Neumann boundary-value problems with…

We obtain analytic solutions for the one-dimensional Dirac equation with the Morse potential as an infinite series of square integrable functions. These solutions are for all energies, the discrete as well as the continuous. The elements of…

We consider Schr\"{o}dinger equations with linearly energy-depending potentials which are compactly supported on the half-line. We first provide estimates of the number of eigenvalues and resonances for such complex-valued potentials under…

The Hodge equations for 1-forms are studied on Beltrami's projective disc model for hyperbolic space. Ideal points lying beyond projective infinity arise naturally in both the geometric and analytic arguments. An existence theorem for…

Let $(M,g)$ be an asymptotically conical Riemannian manifold having dimension $n\ge 2$, opening angle $\alpha \in (0,\pi/2) \setminus \{\arcsin \frac{1}{2k+1}\}_{k \in \mathbb{N}}$ and positive asymptotic rate. Under the assumption that the…

We study a class of $p$-Laplacian Dirichlet problems with weights that are possibly singular on the boundary of the domain, and obtain nontrivial solutions using Morse theory. In the absence of a direct sum decomposition, we use a…

We deal with a boundary value problem of the form $-\epsilon(\phi_p(\epsilon u'))'+a(x)W'(u)=0,\quad u'(0)=0=u'(1),$ where $\phi_p(s) = \vert s \vert^{p-2} s$ for $s \in \mathbb{R}$ and $p>1$, and $W:[-1,1] \to {\mathbb R}$ is a double-well…

We deal with a weakly coupled system of ODEs of the type $$ x_j'' + n_j^2 \,x_j + h_j(x_1,\ldots,x_d) = p_j(t), \qquad j=1,\ldots,d, $$ with $h_j$ locally Lipschitz continuous and bounded, $p_j$ continuous and $2\pi$-periodic, $n_j \in…

We study the asymptotic Dirichlet problem for the minimal graph equation on a Cartan-Hadamard manifold $M$ whose radial sectional curvatures outside a compact set satisfy an upper bound $$K(P)\le - \frac{\phi(\phi-1)}{r(x)^2}$$ and a…

In this article, we study the impact of a change in the type of boundary conditions of an elliptic boundary value problem. In the context of the conductivity equation we consider a reference problem with mixed homogeneous Dirichlet and…

We study the existence of a solution to the mixed boundary value problem for Helmholtz and Poisson type equations in a bounded Lipschitz domain $\Omega\subset\mathbb{R}^N$ and in $\mathbb{R}^N\setminus\Omega$ for $N\geq3$. The boundary…

We consider the large-$N$ asymptotics of a system of discrete orthogonal polynomials on an infinite regular lattice of mesh $\frac{1}{N}$, with weight $e^{-NV(x)}$, where $V(x)$ is a real analytic function with sufficient growth at…

We establish the decay of the solutions of the damped wave equations in one dimensional space for the Dirichlet, Neumann, and dynamic boundary conditions where the damping coefficient is a function of space and time. The analysis is based…

In this paper, we study the Dirichlet boundary value problem of steady-state relativistic Boltzmann equation in half-line with hard potential model, given the data for the outgoing particles at the boundary and a relativistic global…

We study the polyharmonic Neumann and mixed boundary value problems on the Kor\'{a}nyi ball in the Heisenberg group $\H_n$. Necessary and sufficient solvability conditions are obtained for the nonhomogeneous polyharmonic Neumann problem and…

We investigate the asymptotic behavior of solutions of Hamilton-Jacobi equations with large drift term in an open subset of two-dimensional Euclidean space. When the drift is given by $\varepsilon^{-1} (H_{x_2}, -H_{x_1})$ of a Hamiltonian…

We consider the Dirichlet boundary value problem for graphical maximal submanifolds inside Lorentzian type ambient spaces, and obtain general existence and uniqueness results which apply to any codimension.

For the equation (-\Delta u = | |x|-2 |^\alpha u^{p-1}), (1 < |x| < 3), we prove the existence of two solutions for (\alpha) large, and of two additional solutions when (p) is close to the critical Sobolev exponent (2^*=2N/(N-2)). A…