相关论文: Linearized eigenvalues for a free boundary problem…
In this paper, we consider eigenvalues to the following double phase problem with unbalanced growth and indefinite weight, $$ -\Delta_p^a u-\Delta_q u =\lambda m(x) |u|^{q-2}u \quad \mbox{in} \,\, \R^N, $$ where {$N \geq 2$}, {$1<p, q<N$,…
This paper analyzes the structure of the set of nodal solutions of a class of one-dimensional superlinear indefinite boundary values problems with an indefinite weight functions in front of the spectral parameter. Quite astonishingly, the…
This paper presents a method for computing eigenvalues and eigenvectors for some types of nonlinear eigenvalue problems. The main idea is to approximate the functions involved in the eigenvalue problem by rational functions and then apply a…
In this paper, we analyze an eigenvalue problem for nonlinear elliptic operators involving homogeneous Dirichlet boundary conditions in a open smooth bounded domain. We prove bifurcation results from trivial solutions and from infinity for…
We consider a biphasic continuum model for avascular tumour growth in two spatial dimensions, in which a cell phase and a fluid phase follow conservation of mass and momentum. A limiting nutrient that follows a diffusion process controls…
A distributed optimal control problem for a phase field system which physical context is that of tumor growth is discussed. The system we are going to take into account consists of a Cahn-Hilliard equation for the phase variable (relative…
We consider higher-dimensional generalizations of the normalized Laplacian and the adjacency matrix of graphs and study their eigenvalues for the Linial-Meshulam model $X^k(n,p)$ of random $k$-dimensional simplicial complexes on $n$…
We are concerned with the global bifurcation analysis of positive solutions to free boundary problems arising in plasma physics. We show that in general, in the sense of domain variations, the following alternative holds: either the shape…
We introduce a nonlinear and nonlocal model that describes the range expansion of a population resulting from growth and competition for space. This type of phenomenon underlies the expansion of colonies of immotile cells which motivated…
In this paper, we are interested in studying the multiplicity, uniqueness, and nonexistence of solutions for a class of singular elliptic eigenvalue problem for the Dirichlet fractional $(p,q)$-Laplacian. The nonlinearity considered…
We consider an eigenvalue problem for a double-phase differential operator with unbalanced growth. Using the Nehari method, we show that the problem has a continuous spectrum determined by the minimal eigenvalue of the weighted p-Laplacian.
We study an eigenvalue problem involving a degenerate and singular elliptic operator on the whole space $\mathbb{R}^N$. We prove the existence of an unbounded and increasing sequence of eigenvalues. Our study generalizes to the case of…
In the present work we shall consider the existence and multiplicity of solutions for nonlocal elliptic singular problems where the nonlinearity is driven by two convolutions terms. More specifically, we shall consider the following…
This paper is devoted to the proof of the existence of the principal eigenvalue and related eigenfunctions for fully nonlinear uniformly elliptic equations posed in a punctured ball, in presence of a singular potential. More precisely, we…
In this paper, we investigate a system of two nonlinear partial differential equations, arising from a model of cellular proliferation which describes the production of blood cells in the bone marrow. Due to cellular replication, the two…
This paper presents the generalized Fourier series solution for the longitudinal vibrations of a bar subjected to viscous boundary conditions at each end. The model of the system produces a non-selfadjoint eigenvalue problem which does not…
Eigenvalue problems arise in many areas of physics, from solving a classical electromagnetic problem to calculating the quantum bound states of the hydrogen atom. In textbooks, eigenvalue problems are defined for linear problems,…
This paper concerns a distributed optimal control problem for a tumor growth model of Cahn-Hilliard type including chemotaxis with possibly singular potentials, where the control and state variables are nonlinearly coupled. First, we…
We study a class of nonlinear eigenvalue problems which involves a convolution operator as well as a superlinear nonlinearity. Our variational existence proof is based on constrained optimization and provides a one-parameter family of…
In this paper we analyze an eigenvalue problem associated to fractional operators of the form \[ L_a^s u(x)=2 \text{p.v.}\int_{\mathbb{R}^n}a(x,y,D^su(x,y))\,\frac{dy}{|x-y|^{n+s}},\] which represents a generalization model for nonlocal,…