Maximum principles for a class of semilinear elliptic boundary-value problems

For years it has remained a problem to find suitable functionals satisfying certain maximum principles for solutions of the equation Δu + f(x, u) = 0. In this paper, maximum principles for certain functionals which are defined on solutions of semilinear elliptic equations subject to mixed or Robin boundary conditions are obtained. The principles derived may be used to deduce bounds on important quantities in physical problems of interest.

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Semilinear elliptic boundary value problems with nonlinear oblique boundary conditions, a boundary element monotone iteration approach

Variational Methods: Open Problems, Recent Progress, and Numerical Algorithms - Contemporary Mathematics ◽

10.1090/conm/357/06510 ◽

2004 ◽

pp. 17-48

Author(s):

Goong Chen ◽

Yuanhua Deng ◽

Wei-Ming Ni ◽

Jianxin Zhou

Keyword(s):

Boundary Conditions ◽

Boundary Value Problems ◽

Boundary Element ◽

Elliptic Boundary ◽

Boundary Value ◽

Elliptic Boundary Value Problems ◽

Elliptic Boundary Value ◽

Monotone Iteration ◽

Semilinear Elliptic ◽

Oblique Boundary

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Global bifurcation results for semilinear elliptic boundary value problems with indefinite weights and nonlinear boundary conditions

Nonlinear Differential Equations and Applications NoDEA ◽

10.1007/s00030-010-0056-3 ◽

2010 ◽

Vol 17 (3) ◽

pp. 323-336 ◽

Cited By ~ 10

Author(s):

Kenichiro Umezu

Keyword(s):

Boundary Conditions ◽

Boundary Value Problems ◽

Nonlinear Boundary ◽

Elliptic Boundary ◽

Global Bifurcation ◽

Nonlinear Boundary Conditions ◽

Elliptic Boundary Value Problems ◽

Elliptic Boundary Value ◽

Semilinear Elliptic ◽

Indefinite Weights

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On the Stability of Solutions of Semilinear Elliptic Equations with Robin Boundary Conditions on Riemannian Manifolds

SIAM Journal on Mathematical Analysis ◽

10.1137/15m102647x ◽

2016 ◽

Vol 48 (1) ◽

pp. 122-151 ◽

Cited By ~ 7

Author(s):

C. Bandle ◽

P. Mastrolia ◽

D. D. Monticelli ◽

F. Punzo

Keyword(s):

Boundary Conditions ◽

Riemannian Manifolds ◽

Elliptic Equations ◽

Semilinear Elliptic Equations ◽

Robin Boundary Conditions ◽

Stability Of Solutions ◽

Semilinear Elliptic ◽

The Stability ◽

Robin Boundary

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Maximum principles for functionals associated with the solution of semilinear elliptic boundary value problems

Zeitschrift für angewandte Mathematik und Physik ◽

10.1007/bf00945009 ◽

1989 ◽

Vol 40 (3) ◽

pp. 330-338 ◽

Cited By ~ 2

Author(s):

J. R. L. Webb

Keyword(s):

Boundary Value Problems ◽

Elliptic Boundary ◽

Boundary Value ◽

Elliptic Boundary Value Problems ◽

Maximum Principles ◽

Elliptic Boundary Value ◽

Semilinear Elliptic

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On solvability of elliptic boundary value problems via global invertibility

Opuscula Mathematica ◽

10.7494/opmath.2020.40.1.37 ◽

2020 ◽

Vol 40 (1) ◽

pp. 37-47

Author(s):

Michał Bełdziński ◽

Marek Galewski

Keyword(s):

Boundary Conditions ◽

Boundary Value Problems ◽

Elliptic Equations ◽

Dirichlet Boundary ◽

Elliptic Boundary ◽

Boundary Value ◽

Elliptic Boundary Value Problems ◽

Dirichlet Boundary Conditions ◽

Elliptic Boundary Value ◽

Global Invertibility

In this work we apply global invertibility result in order to examine the solvability of elliptic equations with both Neumann and Dirichlet boundary conditions.

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Semilinear elliptic equations having asymptotic limits at zero and infinity

Abstract and Applied Analysis ◽

10.1155/s1085337599000159 ◽

1999 ◽

Vol 4 (4) ◽

pp. 231-242 ◽

Cited By ~ 1

Author(s):

Kanishka Perera ◽

Martin Schechter

Keyword(s):

Boundary Value Problems ◽

Elliptic Equations ◽

Nonlinear Term ◽

Elliptic Boundary ◽

Boundary Value ◽

Elliptic Boundary Value Problems ◽

Semilinear Elliptic Equations ◽

Nontrivial Solutions ◽

Elliptic Boundary Value ◽

Semilinear Elliptic

We obtain nontrivial solutions for semilinear elliptic boundary value problems having resonance both at zero and at infinity, when the nonlinear term has asymptotic limits.

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