Full discretization of a nonlinear parabolic problem containing volterra operators and an unknown dirichlet boundary condition

2015 ◽  
Vol 31 (5) ◽  
pp. 1444-1460 ◽  
Author(s):  
Marijke Grimmonprez ◽  
Marián Slodička
Keyword(s):  
Boundary Condition ◽  
Dirichlet Boundary Condition ◽  
Parabolic Problem ◽  
Dirichlet Boundary ◽  
Full Discretization ◽  
Nonlinear Parabolic Problem ◽  
Nonlinear Parabolic ◽  
Volterra Operators

scholarly journals On some classes of generalized Schrödinger equations

2020 ◽  
Vol 10 (1) ◽  
pp. 522-533
Author(s):  
Amanda S. S. Correa Leão ◽  
Joelma Morbach ◽  
Andrelino V. Santos ◽  
João R. Santos Júnior
Keyword(s):  
Boundary Condition ◽  
Dirichlet Boundary Condition ◽  
Dirichlet Boundary ◽  
Laplacian Operator ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nontrivial Solutions ◽  
Homogeneous Dirichlet Boundary Condition ◽  
Stationary Problems

Abstract Some classes of generalized Schrödinger stationary problems are studied. Under appropriated conditions is proved the existence of at least 1 + $\begin{array}{} \sum_{i=2}^{m} \end{array}$ dim Vλi pairs of nontrivial solutions if a parameter involved in the equation is large enough, where Vλi denotes the eigenspace associated to the i-th eigenvalue λi of laplacian operator with homogeneous Dirichlet boundary condition.

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