Existence theorems, qualitative results and a priori bounds for a class of nonlinear Dirichlet problems

1975 ◽  
Vol 58 (3) ◽  
pp. 219-238 ◽  
Author(s):  
Catherine Bandle
Keyword(s):  
Existence Theorems ◽  
A Priori ◽  
Dirichlet Problems ◽  
A Priori Bounds

scholarly journals A priori bounds for periodic solutions of a delay Rayleigh equation with damping

2003 ◽  
Vol 34 (3) ◽  
pp. 293-298
Author(s):  
Gen-Qiang Wang ◽  
Sui Sun Cheng
Keyword(s):  
Periodic Solutions ◽  
Existence Theorems ◽  
A Priori ◽  
Continuation Theorem ◽  
Rayleigh Equation ◽  
A Priori Bounds ◽  
Mawhin’S Continuation Theorem ◽  
Equation With Delay

A priori bounds are established for periodic solutions of a Rayleigh equation with delay and damping. Such bounds are useful since existence theorems for periodic solutions can then be obtained by means of Mawhin's continuation theorem.

scholarly journals An Application of Potential Estimates to A Priori Bounds for Elliptic Equations

2016 ◽  
Vol 2016 ◽  
pp. 1-6
Author(s):  
Farman Mamedov ◽  
Sara Monsurrò ◽  
Maria Transirico
Keyword(s):  
Elliptic Equations ◽  
A Priori ◽  
Dirichlet Problems ◽  
A Priori Bounds ◽  
Potential Estimate

A potential estimate type approach is used in order to obtain some a priori bounds for the solutions of certain classes of Dirichlet problems associated with nondivergence structure elliptic equations.

scholarly journals A priori bounds of the solution of a one point IBVP for a singular fractional evolution equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Said Mesloub ◽  
Hassan Eltayeb Gadain
Keyword(s):  
Differential Equations ◽  
Evolution Equation ◽  
A Priori Estimates ◽  
Boundary Value ◽  
A Priori ◽  
Initial Boundary ◽  
A Priori Bounds ◽  
Fractional Evolution Equation ◽  
Priori Estimates ◽  
Initial Boundary Value

Abstract A priori bounds constitute a crucial and powerful tool in the investigation of initial boundary value problems for linear and nonlinear fractional and integer order differential equations in bounded domains. We present herein a collection of a priori estimates of the solution for an initial boundary value problem for a singular fractional evolution equation (generalized time-fractional wave equation) with mass absorption. The Riemann–Liouville derivative is employed. Results of uniqueness and dependence of the solution upon the data were obtained in two cases, the damped and the undamped case. The uniqueness and continuous dependence (stability of solution) of the solution follows from the obtained a priori estimates in fractional Sobolev spaces. These spaces give what are called weak solutions to our partial differential equations (they are based on the notion of the weak derivatives). The method of energy inequalities is used to obtain different a priori estimates.

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