scholarly journals Semilinear elliptic equations with the primitive of the nonlinearity interacting with the first eigenvalue

1991 ◽  
Vol 156 (2) ◽  
pp. 381-394 ◽  
Author(s):  
Djairo G de Figueiredo ◽  
Ivar Massabò
Keyword(s):  
Elliptic Equations ◽  
Semilinear Elliptic Equations ◽  
First Eigenvalue ◽  
The First Eigenvalue ◽  
Semilinear Elliptic

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.

On a maximum principle for a class of fourth-order semilinear elliptic equations

1977 ◽  
Vol 77 (3-4) ◽  
pp. 319-323 ◽  
Author(s):  
Philip W. Schaefer
Keyword(s):  
Elliptic Equations ◽  
Existence Of Solutions ◽  
Linear Partial Differential Equation ◽  
First Eigenvalue ◽  
Dirichlet Eigenvalue ◽  
The First Eigenvalue ◽  
Semilinear Elliptic ◽  
Maximum Value ◽  
Non Linear ◽  
Dirichlet Eigenvalue Problem

SynopsisIt is shown that Ф = | grad u |2–uΔu, where u is a solution of Δ2u+pf(u) = 0 in D, assumes its maximum value on the boundary of D. This principle leads one to a lower bound on the first eigenvalue in the non-linear Dirichlet eigenvalue problem and to the non-existence of solutions to this non-linear partial differential equation subject to certain zero boundaryconditions.

scholarly journals Nonexistence Results of Semilinear Elliptic Equations Coupled with the Chern-Simons Gauge Field

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
Hyungjin Huh
Keyword(s):  
Gauge Field ◽  
Elliptic Equations ◽  
Semilinear Elliptic Equations ◽  
Schrodinger Equations ◽  
Schrödinger Equations ◽  
Nontrivial Solutions ◽  
Semilinear Elliptic ◽  
Chern Simons

We discuss the nonexistence of nontrivial solutions for the Chern-Simons-Higgs and Chern-Simons-Schrödinger equations. The Derrick-Pohozaev type identities are derived to prove it.

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