scholarly journals ASYMPTOTICS OF SOLUTION OF THE SINGULARLY PERTURBED DIRICHLET PROBLEM WITH A WEAK CRITICAL POINT

2018 ◽  
Vol 10 (1) ◽  
pp. 21-26
Author(s):  
D.A. Tursunov ◽  
◽  
K. Alymkulov ◽  
B.A. Azimov ◽  
◽  
...  
Keyword(s):  
Dirichlet Problem ◽  
Critical Point ◽  
Singularly Perturbed ◽  
Asymptotics Of Solution

scholarly journals Three Solutions for Inequalities Dirichlet Problem Driven byp(x)-Laplacian-Like

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Zhou Qing-Mei ◽  
Ge Bin
Keyword(s):  
Dirichlet Problem ◽  
Critical Point ◽  
Point Theorem ◽  
Elliptic Problems ◽  
Nonlinear Elliptic Problems ◽  
Three Solutions ◽  
Critical Point Theorem ◽  
Nonlinear Elliptic ◽  
Locally Lipschitz

A class of nonlinear elliptic problems driven byp(x)-Laplacian-like with a nonsmooth locally Lipschitz potential was considered. Applying the version of a nonsmooth three-critical-point theorem, existence of three solutions of the problem is proved.

On the profile of solutions with two sharp layers to a singularly perturbed semilinear Dirichlet problem

1997 ◽  
Vol 127 (4) ◽  
pp. 691-701 ◽  
Author(s):  
E. N. Dancer ◽  
Juncheng Wei
Keyword(s):  
Boundary Layer ◽  
Dirichlet Problem ◽  
Positive Solutions ◽  
Elliptic Equations ◽  
Singularly Perturbed ◽  
Convex Domains ◽  
Existence Of Positive Solutions

We discuss the existence of positive solutions of some singularity perturbed elliptic equations on convex domains with nonlinearity changing sign. In particular, we obtain solutions with both a boundary layer and a sharp interior peak.

scholarly journals Existence results for nonlinear elliptic problems on fractal domains

2016 ◽  
Vol 5 (1) ◽  
Author(s):  
Massimiliano Ferrara ◽  
Giovanni Molica Bisci ◽  
Dušan Repovš
Keyword(s):  
Weak Solution ◽  
Dirichlet Problem ◽  
Critical Point ◽  
Elliptic Problems ◽  
Open Interval ◽  
Existence Results ◽  
Nonlinear Elliptic Problems ◽  
Nonlinear Elliptic ◽  
Fractal Domains ◽  
Critical Point Result

AbstractSome existence results for a parametric Dirichlet problem defined on the Sierpiński fractal are proved. More precisely, a critical point result for differentiable functionals is exploited in order to prove the existence of a well-determined open interval of positive eigenvalues for which the problem admits at least one non-trivial weak solution.

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