scholarly journals Topological degree and applications to elliptic problems with discontinuous nonlinearity

2017 ◽  
Vol 10 (02) ◽  
pp. 612-624
Author(s):  
In-Sook Kim
Keyword(s):  
Topological Degree ◽  
Elliptic Problems ◽  
Discontinuous Nonlinearity

Existence and multiplicity of solutions for discontinuous elliptic problems in ℝ N

2020 ◽  
pp. 1-25
Author(s):  
Claudianor O. Alves ◽  
Ziqing Yuan ◽  
Lihong Huang
Keyword(s):  
Variational Principle ◽  
Variational Methods ◽  
Multiple Solutions ◽  
Elliptic Problems ◽  
Ekeland’S Variational Principle ◽  
Discontinuous Nonlinearity ◽  
Nontrivial Solutions ◽  
Ekeland's Variational Principle ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity

Abstract This paper concerns with the existence of multiple solutions for a class of elliptic problems with discontinuous nonlinearity. By using dual variational methods, properties of the Nehari manifolds and Ekeland's variational principle, we show how the ‘shape’ of the graph of the function A affects the number of nontrivial solutions.

scholarly journals Existence and Concentration of Solutions for a Class of Elliptic Problems with Discontinuous Nonlinearity in $\mathbf{R}^{N}$

2013 ◽  
Vol 112 (1) ◽  
pp. 129 ◽  
Author(s):  
Claudianor O. Alves ◽  
Rúbia G. Nascimento
Keyword(s):  
Variational Methods ◽  
Positive Solutions ◽  
Elliptic Problems ◽  
Discontinuous Nonlinearity ◽  
Concentration Of Solutions

Using variational methods we establish existence and concentration of positive solutions for a class of elliptic problems in $\mathbf{R}^{N}$, whose nonlinearity is discontinuous.

Multiplicity results for a nonlinear Dirichlet problem

1984 ◽  
Vol 96 (3-4) ◽  
pp. 331-336
Author(s):  
S. Solimini
Keyword(s):  
Dirichlet Problem ◽  
Topological Degree ◽  
Linear Problem ◽  
Elliptic Problems ◽  
Main Tool ◽  
Multiplicity Results ◽  
Nonlinear Dirichlet Problem ◽  
Jumping Nonlinearities

SynopsisThis paper deals with some multiplicity results for elliptic problems with jumping nonlinearities. Our results are concerned with the case in which only one eigenvalue of the linear problem is jumped and it is simple. The main tool used is the Leray–Schauder topological degree. We consider a parametrized problem and prove the existence of two or three distinct solutions for suitable values of the parameter.

scholarly journals On the degree theory for densely defined mappings of class(S+)L

1999 ◽  
Vol 4 (3) ◽  
pp. 141-152 ◽  
Author(s):  
Juha Berkovits
Keyword(s):  
Topological Degree ◽  
Degree Theory ◽  
Elliptic Problems ◽  
Existence Results ◽  
Basic Properties ◽  
New Construction ◽  
Densely Defined ◽  
Monotone Type ◽  
Abstract Existence

We introduce a new construction of topological degree for densely defined mappings of monotone type. We also study the structure of the classes of mappings involved. Using the basic properties of the degree, we prove some abstract existence results that can be applied to elliptic problems.

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