Related papers: Eigenvalues of a third order BVP subject to functi…
We investigate existence and uniqueness of solutions to second-order elliptic boundary value problems containing a power nonlinearity applied to a fractional Laplacian. We detect the critical power separating the existence from the…
We consider a wide class of linear boundary-value problems for systems of $r$-th order ordinary differential equations whose solutions range over the normed complex space $(C^{(n)})^m$ of $n\geq r$ times continuously differentiable…
We investigate the existence of positive solutions to the nonlinear second-order three-point integral boundary value problem \label{eq-1} {u^{\prime \prime}}(t)+a(t)f(u(t))=0,\ 0<t<T, u(0)={\beta}u(\eta),\…
It is developed the theory of the boundary behavior of homeomorphic solutions of the Beltrami equations ${\bar{\partial}}f=\mu\,{\partial}f$ of the Sobolev class $W^{1,1}_{\rm loc}$ with respect to prime ends of domains. On this basis,…
This paper is devoted to the existence of positive solutions for a problem related to a fourth-order differential equation involving a nonlinear term depending on a second order differential operator, $$(-\Delta)^2 u=\lambda u+…
This work is devoted to the study of first order linear problems with involution and periodic boundary value conditions. We first prove a correspondence between a large set of such problems with different involutions to later focus our…
In this paper we study the geometry of certain functionals associated to quasilinear elliptic boundary value problems with a degenerate nonlocal term of Kirchhoff type. Due to the degeneration of the nonlocal term it is not possible to…
We consider the Cauchy problem of third order Benjamin-Ono type equations on the torus. Nonlinear terms may yield derivative losses, which prevents us from using the classical energy method. In order to overcome that difficulty, we add a…
We study boundary value problems associated with singular, strongly nonlinear differential equations with functional terms of type $$\big(\Phi(k(t)\,x'(t))\big)' + f(t,\mathcal{G}_x(t))\,\rho(t, x'(t)) = 0$$ on a compact interval $[a,b]$.…
We show that inverse square singularities can be treated as boundary conditions containing rational Herglotz--Nevanlinna functions of the eigenvalue parameter with "a negative number of poles". More precisely, we treat in a unified manner…
The paper deals with the three-dimensional Dirichlet boundary value problem (BVP) for a second order strongly elliptic self-adjoint system of partial differential equations in the divergence form with variable coefficients and develops the…
Motivated by the study of systems of higher order boundary value problems with functional boundary conditions, we discuss, by topological methods, the solvability of a fairly general class of systems of perturbed Hammerstein integral…
We investigate the Steklov eigenvalue problem in an exterior Euclidean domain. First, we present several formulations of this problem and establish the equivalences between them. Next, we examine various properties of the exterior Steklov…
We consider the operator of taking the $2p$th derivative of a function with zero boundary conditions for the function and its first $p-1$ derivatives at two distinct points. Our main result provides an asymptotic formula for the eigenvalues…
For bounded domains, eigenvalues and eigenfunctions of double layer potentials are considered. The aim of this paper is to establish some relationships between eigenvalues, eigenfunctions and the geometry of domain boundaries.
In this paper, we investigate the Euler-Bernoulli fourth-order boundary value problem (BVP) $w^{(4)}=f(x,w)$, $x\in \intcc{a,b}$, with specified values of $w$ and $w''$ at the end points, where the behaviour of the right-hand side $f$ is…
We study the existence of positive eigenpairs for a class of Caputo fractional autonomous evolution equations with nonlocal initial condition within the framework of Banach lattices. The autonomous linear operator generates a compact…
Recent work in the literature has studied fourth-order elliptic operators on manifolds with boundary. This paper proves that, in the case of the squared Laplace operator, the boundary conditions which require that the eigenfunctions and…
This article concerns on the existence of multiple solutions for a new Kirchhoff-type problem with negative modulus. We prove that there exist three nontrivial solutions when the parameter is enough small via the variational methods and…
In this paper, we study the Hessian equation with infinite Dirichlet (blow-up) boundary value conditions. Using radial functions and techniques of ordinary differential inequality, we construct various barrier functions (super-solution and…