scholarly journals Critical Points for Elliptic Equations with Prescribed Boundary Conditions

2017 ◽  
Vol 226 (1) ◽  
pp. 117-141 ◽  
Author(s):  
Giovanni S. Alberti ◽  
Guillaume Bal ◽  
Michele Di Cristo
Keyword(s):  
Boundary Conditions ◽  
Critical Points ◽  
Elliptic Equations

ON A CLASS OF FOURTH ORDER NONLINEAR ELLIPTIC EQUATIONS UNDER NAVIER BOUNDARY CONDITIONS

2010 ◽  
Vol 08 (02) ◽  
pp. 185-197 ◽  
Author(s):  
F. J. S. A. CORRÊA ◽  
J. V. GONCALVES ◽  
ANGELO RONCALLI
Keyword(s):  
Boundary Conditions ◽  
Fixed Points ◽  
Fourth Order ◽  
Elliptic Equations ◽  
Nonlinear Elliptic Equations ◽  
Compact Operators ◽  
Schmidt Method ◽  
Navier Boundary Conditions ◽  
Nonlinear Elliptic ◽  
Existence And Multiplicity

We employ arguments involving continua of fixed points of suitable nonlinear compact operators and the Lyapunov–Schmidt method to prove existence and multiplicity of solutions in a class of fourth order non-homogeneous resonant elliptic problems. Our main result extends even similar ones known for the Laplacian.

scholarly journals On a class of semilinear elliptic equations with boundary conditions and potentials which change sign

2005 ◽  
Vol 2005 (2) ◽  
pp. 95-104
Author(s):  
M. Ouanan ◽  
A. Touzani
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Elliptic Equations ◽  
First Eigenvalue ◽  
Nontrivial Solutions ◽  
Bounded Smooth Domain ◽  
The First Eigenvalue ◽  
Semilinear Elliptic ◽  
Superlinear Growth ◽  
Bounded Smooth

We study the existence of nontrivial solutions for the problemΔu=u, in a bounded smooth domainΩ⊂ℝℕ, with a semilinear boundary condition given by∂u/∂ν=λu−W(x)g(u), on the boundary of the domain, whereWis a potential changing sign,ghas a superlinear growth condition, and the parameterλ∈]0,λ1];λ1is the first eigenvalue of the Steklov problem. The proofs are based on the variational and min-max methods.

scholarly journals Advanced Design of Packing and Cylinders for Hyper-Compressors for LDPE Production

2005 ◽  
Author(s):  
Enzo Giacomelli ◽  
Franco Graziani ◽  
Simone Pratesi ◽  
Giovanni Zonfrillo ◽  
Iacopo Giovannetti
Keyword(s):  
Boundary Conditions ◽  
Stress Level ◽  
Critical Points ◽  
External Factors ◽  
Simulation Approach ◽  
Interference Fit ◽  
Tie Rods ◽  
Complex Arrangement

The optimization of packing cup geometry is important for improving the reliability of hyper-compressors. The complex arrangement and the transmission of loads through the various components requires the use of FEA to properly determine the stress level. The need to reduce the sensitivity to external factors requires an investigation with more advanced simulations. The entire cylinder and associated components such as head flanges, cylinder chambers and tie rods, were modeled. This provided the characteristics of the interfaces and the boundary conditions necessary to simulate the packing cups. Considering the thickness, ring housing profile, lube-oil holes, mating surfaces, interference-fit and diameter make it possible to obtain the stresses at the most critical points. This new simulation approach shows the effect of the parameters that influence the stress level at critical points, thus optimizing the packing cup profile and its relevant features.

Linear second order elliptic equations with Venttsel boundary conditions

1991 ◽  
Vol 118 (3-4) ◽  
pp. 193-207 ◽  
Author(s):  
Yousong Luo ◽  
Neil S. Trudinger
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Elliptic Equations ◽  
Existence Result ◽  
Boundary Value ◽  
Second Order ◽  
Classical Solutions ◽  
Schauder Estimate ◽  
Second Order Elliptic Equations

SynopsisWe prove a Schauder estimate for solutions of linear second order elliptic equations with linear Venttsel boundary conditions, and establish an existence result for classical solutions for such boundary value problems.

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