A maximum principle for a class of functionals in nonlinear dirichlet problems

1976 ◽  
pp. 400-406
Author(s):  
Philip W. Schaefer ◽  
René P. Sperb
Keyword(s):  
Maximum Principle ◽  
Dirichlet Problems

scholarly journals Weak maximum principle for Dirichlet problems with convection or drift terms

2021 ◽  
Vol 3 (3) ◽  
pp. 1-9
Author(s):  
Lucio Boccardo ◽  
◽  
◽  
◽  
Keyword(s):  
Maximum Principle ◽  
Dirichlet Problems ◽  
Weak Maximum Principle ◽  
Drift Terms

Strong Maximum Principle for Some Quasilinear Dirichlet Problems Having Natural Growth Terms

2020 ◽  
Vol 20 (2) ◽  
pp. 503-510
Author(s):  
Lucio Boccardo ◽  
Luigi Orsina
Keyword(s):  
Maximum Principle ◽  
Elliptic Equations ◽  
Strong Maximum Principle ◽  
Quasilinear Elliptic Equations ◽  
Quadratic Growth ◽  
Natural Growth ◽  
Dirichlet Problems ◽  
Natural Growth Terms ◽  
Quasilinear Elliptic ◽  
Lower Order Terms

AbstractIn this paper, dedicated to Laurent Veron, we prove that the Strong Maximum Principle holds for solutions of some quasilinear elliptic equations having lower order terms with quadratic growth with respect to the gradient of the solution.

scholarly journals Three solutions to Dirichlet problems for second-order self-adjoint difference equations involving p-Laplacian

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Feng Xiong ◽  
Zhan Zhou
Keyword(s):  
Dirichlet Problem ◽  
Maximum Principle ◽  
Difference Equation ◽  
Difference Equations ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Strong Maximum Principle ◽  
Second Order ◽  
Dirichlet Problems ◽  
Three Solutions

AbstractThis paper derives several sufficient conditions for the existence of three solutions to the Dirichlet problem for a second-order self-adjoint difference equation involving p-Laplacian through the critical point theory. Furthermore, by using the strong maximum principle, we prove that the three solutions are positive under appropriate assumptions on the nonlinearity. Finally, we present three examples to confirm our results.

Dynamics Response Control of a Mindlin-Type Beam

2017 ◽  
Vol 17 (03) ◽  
pp. 1750039 ◽  
Author(s):  
Kenan Yildirim ◽  
Seda G. Korpeoglu ◽  
Ismail Kucuk
Keyword(s):  
Optimal Control ◽  
Partial Differential Equations ◽  
Maximum Principle ◽  
Control Problem ◽  
Control Function ◽  
Initial Boundary ◽  
Response Control ◽  
Adjoint Variables ◽  
Dynamics Response ◽  
Optimal Control Function

Optimal boundary control for damping the vibrations in a Mindlin-type beam is considered. Wellposedness and controllability of the system are investigated. A maximum principle is introduced and optimal control function is obtained by means of maximum principle. Also, by using maximum principle, control problem is reduced to solving a system of partial differential equations including state, adjoint variables, which are subject to initial, boundary and terminal conditions. The solution of the system is obtained by using MATLAB. Numerical results are presented in table and graphical forms.

The Continuous Maximum Principle

1967 ◽  
Vol 18 (3) ◽  
pp. 332-333
Author(s):  
K. B. Haley
Keyword(s):  
Maximum Principle

scholarly journals Local versus nonlocal elliptic equations: short-long range field interactions

2020 ◽  
Vol 10 (1) ◽  
pp. 895-921
Author(s):  
Daniele Cassani ◽  
Luca Vilasi ◽  
Youjun Wang
Keyword(s):  
Asymptotic Behavior ◽  
Maximum Principle ◽  
Weak Solutions ◽  
Elliptic Equations ◽  
Spectral Properties ◽  
Fractional Laplacian ◽  
Coupling Parameter ◽  
Nonlocal Operators ◽  
The Maximum Principle ◽  
Regularity Results

Abstract In this paper we study a class of one-parameter family of elliptic equations which combines local and nonlocal operators, namely the Laplacian and the fractional Laplacian. We analyze spectral properties, establish the validity of the maximum principle, prove existence, nonexistence, symmetry and regularity results for weak solutions. The asymptotic behavior of weak solutions as the coupling parameter vanishes (which turns the problem into a purely nonlocal one) or goes to infinity (reducing the problem to the classical semilinear Laplace equation) is also investigated.

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