Search · four archives
Search · four archives
21 papers · ranked by Valyu relevance
Julián López-Gómez, Alejandro Sahuquillo, Andrea Tellini
The first goal of this paper is to establish the existence of a positive solution for the singular boundary value problem (1.1), where B is a general boundary operator of Dirichlet, Neumann or Robin type, either classical or non-classical; in the sense that, as soon as Bu(0) = −u ′ (0) + βu(0), the coefficient β can…
Nicola Abatangelo, David Gómez‐Castro, Juan Luis Vázquez
We perform a unified analysis for the boundary behaviour of solutions to nonlocal fractional equations posed in bounded domains. Based on previous findings for some models of the fractional Laplacian operator, we show how it strongly differs from the boundary behaviour of solutions to elliptic problems modelled upon…
Bandyopadhyay, Shalmali, Kunkel, Curtis J
We explore singular second-order boundary value problems with mixed boundary conditions on a general time scale. Using the lower and upper solutions method combined with the Brouwer fixed point theorem we demonstrate the existence of a positive solution and obtain the desired solution by using a sequence of solutions…
Takashi Kagaya
In this paper, we deal with the initial value problem for a class of fully nonlinear parabolic equations with a singular Dirichlet boundary condition in one space dimension. The interior equation includes, for example, a fully nonlinear p-Laplace type heat equation and a β-power type curvature flow. The singular…
Petru Jebelean
where φ is a homeomorphism from Ba – the open ball of radius a centered at 0RN , onto R N , satisfying φ(0RN ) = 0RN , φ = ∇Φ, with Φ : Ba → (−∞, 0] of class C 1 on Ba, continuous and strictly convex on Ba. The potential F : [0, T ] × R N → R is of class C 1 with respect to the second variable and j : R N × R N → (−∞…
Zulqurnain Sabir, Thongchai Botmart, Muhammad Asif Zahoor Raja, Wajaree Weera + 2 more
'Wajaree Weera' 'Fevzi Erdoğan' 'Dragan Pamucar'] In the present study, a neuro-evolutionary scheme is presented for solving a class of singular singularly perturbed boundary value problems (SSP-BVPs) by manipulating the strength of feed-forward artificial neural networks (ANNs), global search particle swarm…
Ewa Bednarczuk, Olga Brezhneva, Krzysztof Leśniewski, Agnieszka Prusińska + 2 more
'Agnieszka Prusińska' 'Alexey A. Tret’yakov' 'Carlo Cattani'] We present recent advances in the analysis of nonlinear problems involving singular (degenerate) operators. The results are obtained within the framework of p-regularity theory, which has been successfully developed over the past four decades. We illustrate…
Gemadi Roba Kusi, Aknaw Hailemariam Habte, Tesfaye Aga Bullo
Singularly perturbed parabolic convection-diffusion problem with interior layer is a type of singularly perturbed boundary value problems which have sign change properties in the coefficient function of the convection term. This paper introduces a layer resolving numerical scheme for solving the numerical solution of…
Sucheta Ghosh, Shankar Prasad Bhattacharyya
The quantum states of hydrogen atom in one dimension can be obtained by a careful application of the well-known Frobenius method. The exercise is highly educative and brings to focus the subtle aspects of quantum mechanics. The allowed states turn out to be only of odd parity and non-degenerate, having energy given by…
Meena Joshi, Anita Tomar, Mohammad Sajid, S.K. Padaliya
In the present study, a novel version of the contraction theory on a relational partial metric space associated with a binary relation is exhibited. In this process, we observe that numerous relations can be used in many well-known fixed point theorems earlier introduced by multiple authors. We solve an elliptic…
Ababi Hailu Ejere, Gemechis File Duressa, Mesfin Mekuria Woldaregay, Tekle Gemechu Dinka
'Tekle Gemechu Dinka'] In this study, a parameter-uniform numerical scheme is built and analyzed to treat a singularly perturbed parabolic differential equation involving large spatial delay. The solution of the considered problem has two strong boundary layers due to the effect of the perturbation parameter, and the…
Aklilu Fufa Oljira, Mesfin Mekuria Woldaregay
Objectives In this paper, a uniformly convergent numerical scheme is proposed for solving a singularly perturbed Fredholm integro-differential equation with an integral initial condition. The equation involves a left boundary layer which makes it difficult to solve it using the standard numerical methods. A fitted…
Nikos I. Kavallaris, Farrukh Javed
We introduce a mechanistic, nonlocal tumour-growth model designed specifically to capture explosive dynamics that are not adequately explained by standard logistic reaction–diffusion descriptions. The motivation is empirical: the universal scaling law reported in [1] provides compelling cross-sectional evidence of…
Julián López-Gómez, Pierpaolo Omari
Here, u 0 / p 1 + (u0) 2 0 is the one-dimensional curvature operator, λ ∈ R is a parameter, the weight a(x) changes sign, and, in most occasions, the function f(u) has a sublinear potential F(u) at ∞. Our discussion displays the manifold patterns occurring for these solutions, depending on the behavior of the potential…
Ray Zirui Zhang, Christopher E. Miles, Xiaohui Xie, John S. Lowengrub
We propose a new neural network based method for solving inverse problems for partial differential equations (PDEs) by formulating the PDE inverse problem as a bilevel optimization problem. At the upper level, we minimize the data loss with respect to the PDE parameters. At the lower level, we train a neural network to…
Pilar Herreros
We also use this functional to construct nonlinearities f such that this problem has at least two bound state solutions that change sign j times, for j = 1, . . . , k − 1. And another f such that this problem has a unique ground state solution, and at least two bound state solutions that change sign one time.
Nasireh Dayarian, Ali Khadem
This article presents a hybrid boundary element-finite element (BE-FE) method to solve the EEG forward problem and take advantages of both the boundary element method (BEM) and finite element method (FEM). Although realistic EEG forward problems with heterogeneous and anisotropic regions can be solved by FEM…
Ali Feizmohammadi, Yavar Kian, Lauri Oksanen
We consider the inverse problem of determining coefficients appearing in semilinear elliptic equations stated on Riemannian manifolds with boundary given the knowledge of the associated Dirichlet-to-Neumann map. We begin with a negative answer to this problem. Owing to this obstruction, we consider a new formulation of…
Authors not listed
This article is the second in a two-part tutorial review on electronic spin-dependent dynamics. In Part I, we presented the fundamental theory within the adiabatic Born– Huang framework that describes the interaction between nuclear motion and the elec- tronic (spin and spatial) degrees of freedom. In particular, we…
Emine Atıcı Endes, Neslihan Nesliye Pelen
Atherosclerotic plaques are fatty deposits in arterial walls and a major cause of heart attacks and strokes. Macrophage proliferation triggers plaque growth and instability, but the specific conditions that convert stable plaques into unstable ones remain unclear. To provide insight into the conditions for this…
David Thompson, Johan Gielis
Our understanding of quantum phenomena often begins with simple particle-in-a-box style problems, the solutions of which introduce the student to foundational quantum concepts such as degeneracy and quantization. Simple model geometries of confinement afford analytic solutions, which are readily derivable, easily…