sublinear perturbation
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scholarly journals Fourth-order elliptic problems with critical nonlinearities by a sublinear perturbation

2021 ◽  
Vol 26 (2) ◽  
pp. 227-240
Author(s):  
Lin Li ◽  
Donal O’Regan
Keyword(s):  
Boundary Condition ◽  
Positive Solutions ◽  
Fourth Order ◽  
Local Minimum ◽  
Elliptic Problems ◽  
Order Problem ◽  
Critical Nonlinearities ◽  
Fourth Order Problem ◽  
Minimum Theorem ◽  
Sublinear Perturbation

In this paper, we get the existence of two positive solutions for a fourth-order problem with Navier boundary condition. Our nonlinearity has a critical growth, and the method is a local minimum theorem obtained by Bonanno.

Fractional problems with critical nonlinearities by a sublinear perturbation

2020 ◽  
Vol 23 (2) ◽  
pp. 484-503 ◽  
Author(s):  
Lin Li ◽  
Stepan Tersian
Keyword(s):  
Critical Exponent ◽  
Variational Approach ◽  
Local Minimum ◽  
Numerical Estimate ◽  
Nontrivial Solutions ◽  
The Real ◽  
Critical Nonlinearities ◽  
Minimum Theorem ◽  
Sublinear Perturbation

AbstractIn this paper, the existence of two nontrivial solutions for a fractional problem with critical exponent, depending on real parameters, is established. The variational approach is used based on a local minimum theorem due to G. Bonanno. In addition, a numerical estimate on the real parameters is provided, for which the two solutions are obtained.

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