scholarly journals On the viscous Cahn–Hilliard–Oono system with chemotaxis and singular potential

2021 ◽  
Author(s):  
Jingning He
Keyword(s):  
Singular Potential

scholarly journals On Scattering and Bound States for a Singular Potential

1970 ◽  
Vol 43 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Erasmo Ferreira ◽  
Javier Sesma ◽  
Pedro L. Torres
Keyword(s):  
Bound States ◽  
Singular Potential

Heat equation with singular potential and singular data

2005 ◽  
Vol 135 (4) ◽  
pp. 863-886 ◽  
Author(s):  
M. Nedeljkov ◽  
S. Pilipović ◽  
D. Rajter-Ćirić
Keyword(s):  
Polynomial Growth ◽  
Singular Potential ◽  
Function Algebra ◽  
Energy Estimates ◽  
Generalized Function ◽  
Type Condition ◽  
Classical Energy ◽  
The Cauchy Problem ◽  
White Noise Calculus ◽  
Singular Data

Nets of Schrödinger C0-semigroups (Sε)ε with the polynomial growth with respect to ε are used for solving the Cauchy problem (∂t − Δ)U + VU = f(t, U), U(0, x) = U0(x) in a suitable generalized function algebra (or space), where V and U0 are singular generalized functions while f satisfies a Lipschitz-type condition. The existence of distribution solutions is proved in appropriate cases by the means of white noise calculus as well as classical energy estimates.

Multiple solutions for semi-linear corner degenerate elliptic equations with singular potential term

2016 ◽  
Vol 19 (04) ◽  
pp. 1650043 ◽  
Author(s):  
Hua Chen ◽  
Shuying Tian ◽  
Yawei Wei
Keyword(s):  
Dirichlet Problem ◽  
Variational Method ◽  
Elliptic Equations ◽  
Multiple Solutions ◽  
Dirichlet Boundary ◽  
Singular Potential ◽  
Degenerate Elliptic Equations ◽  
Dirichlet Boundary Value Problem ◽  
Potential Term ◽  
Degenerate Elliptic

The present paper is concern with the Dirichlet problem for semi-linear corner degenerate elliptic equations with singular potential term. We first give the preliminary of the framework and then discuss the weighted corner type Hardy inequality. By using the variational method, we prove the existence of multiple solutions for the Dirichlet boundary-value problem.

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