scholarly journals Existence and multiplicity of solutions for asymptotically linear nonperiodic Hamiltonian elliptic system

2013 ◽  
Vol 399 (2) ◽  
pp. 433-441 ◽  
Author(s):  
Jian Zhang ◽  
Wenping Qin ◽  
Fukun Zhao
Keyword(s):  
Elliptic System ◽  
Asymptotically Linear ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Hamiltonian Elliptic System

scholarly journals Existence and Multiplicity of Solutions to Discrete Conjugate Boundary Value Problems

2010 ◽  
Vol 2010 ◽  
pp. 1-26
Author(s):  
Bo Zheng
Keyword(s):  
Nonlinear Analysis ◽  
Boundary Value Problems ◽  
Morse Theory ◽  
Boundary Value ◽  
Asymptotically Linear ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Linear Condition ◽  
Concrete Computation ◽  
Special Case

We consider the existence and multiplicity of solutions to discrete conjugate boundary value problems. A generalized asymptotically linear condition on the nonlinearity is proposed, which includes the asymptotically linear as a special case. By classifying the linear systems, we define index functions and obtain some properties and the concrete computation formulae of index functions. Then, some new conditions on the existence and multiplicity of solutions are obtained by combining some nonlinear analysis methods, such as Leray-Schauder principle and Morse theory. Our results are new even for the case of asymptotically linear.

scholarly journals Multiplicity of Solutions for Gradient Systems Using Landesman-Lazer Conditions

2010 ◽  
Vol 2010 ◽  
pp. 1-22 ◽  
Author(s):  
Edcarlos D. da Silva
Keyword(s):  
Eigenvalue Problem ◽  
Variational Methods ◽  
Elliptic System ◽  
Morse Theory ◽  
Critical Groups ◽  
Gradient Systems ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Indefinite Weights

We establish existence and multiplicity of solutions for an elliptic system which presents resonance at infinity of Landesman-Lazer type. In order to describe the resonance, we use an eigenvalue problem with indefinite weights. In all results, we use Variational Methods, Morse Theory and Critical Groups.

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