scholarly journals Multiple solutions for a class of Ambrosetti-Prodi type problems for systems involving critical Sobolev exponents

2008 ◽  
Vol 7 (2) ◽  
pp. 355-372 ◽  
Author(s):  
F. R. Pereira ◽  
Keyword(s):  
Multiple Solutions ◽  
Critical Sobolev Exponents

Existence and asymptotic behavior of standing wave solutions for a class of generalized quasilinear Schrödinger equations with critical Sobolev exponents

2020 ◽  
Vol 120 (3-4) ◽  
pp. 199-248
Author(s):  
Jianhua Chen ◽  
Xianjiu Huang ◽  
Dongdong Qin ◽  
Bitao Cheng
Keyword(s):  
Asymptotic Behavior ◽  
Ground State ◽  
Multiple Solutions ◽  
Global Minimum ◽  
Global Maximum ◽  
Quasilinear Schrödinger Equation ◽  
Critical Sobolev Exponents ◽  
Wave Solutions ◽  
Change Of Variable ◽  
Concentration Behavior

In this paper, we study the following generalized quasilinear Schrödinger equation − div ( ε 2 g 2 ( u ) ∇ u ) + ε 2 g ( u ) g ′ ( u ) | ∇ u | 2 + V ( x ) u = K ( x ) | u | p − 2 u + | u | 22 ∗ − 2 u , x ∈ R N , where N ⩾ 3, ε > 0, 4 < p < 22 ∗ , g ∈ C 1 ( R , R + ), V ∈ C ( R N ) ∩ L ∞ ( R N ) has a positive global minimum, and K ∈ C ( R N ) ∩ L ∞ ( R N ) has a positive global maximum. By using a change of variable, we obtain the existence and concentration behavior of ground state solutions for this problem with critical growth, and establish a phenomenon of exponential decay. Moreover, by Ljusternik–Schnirelmann theory, we also prove the existence of multiple solutions.

An Overview of Risk-Based EEE Counterfeit Part Detection Based on SAE AS6171

2018 ◽  
Author(s):  
Michael H. Azarian
Keyword(s):  
Risk Assessment ◽  
Multiple Solutions ◽  
Test Equipment ◽  
Assessment Methodology ◽  
Test Plan ◽  
Specific Test ◽  
Risk Assessment Methodology

Abstract As counterfeiting techniques and processes grow in sophistication, the methods needed to detect these parts must keep pace. This has the unfortunate effect of raising the costs associated with managing this risk. In order to ensure that the resources devoted to counterfeit detection are commensurate with the potential effects and likelihood of counterfeit part usage in a particular application, a risk based methodology has been adopted for testing of electrical, electronic, and electromechanical (EEE) parts by the SAE AS6171 set of standards. This paper provides an overview of the risk assessment methodology employed within AS6171 to determine the testing that should be utilized to manage the risk associated with the use of a part. A scenario is constructed as a case study to illustrate how multiple solutions exist to address the risk for a particular situation, and the choice of any specific test plan can be made on the basis of practical considerations, such as cost, time, or the availability of particular test equipment.

Multiple Solutions Approach (MSA): Conceptions and Practices of Primary School Teachers in Ghana

2016 ◽  
Vol 2 (2) ◽  
pp. 333
Author(s):  
Michael Johnsn Nabie ◽  
Kolawole Raheem ◽  
John Bijou Agbemaka ◽  
Rufai Sabtiwu
Keyword(s):  
Primary School ◽  
Multiple Solutions ◽  
School Teachers ◽  
Primary School Teachers
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