scholarly journals On the existence of nontrivial solutions for a fourth-order semilinear elliptic problem

2005 ◽  
Vol 2005 (6) ◽  
pp. 673-683
Author(s):  
Aixia Qian ◽  
Shujie Li
Keyword(s):  
Boundary Conditions ◽  
Nontrivial Solution ◽  
Fourth Order ◽  
Elliptic Problem ◽  
Nontrivial Solutions ◽  
Navier Boundary Conditions ◽  
Minimax Theory ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic

By means of Minimax theory, we study the existence of one nontrivial solution and multiple nontrivial solutions for a fourth-order semilinear elliptic problem with Navier boundary conditions.

scholarly journals On the existence of solutions to a fourth-order quasilinear resonant problem

2002 ◽  
Vol 7 (3) ◽  
pp. 125-133 ◽  
Author(s):  
Shibo Liu ◽  
Marco Squassina
Keyword(s):  
Boundary Conditions ◽  
Nontrivial Solution ◽  
Fourth Order ◽  
Elliptic Problem ◽  
Morse Theory ◽  
Existence Of Solutions ◽  
Nontrivial Solutions ◽  
Navier Boundary Conditions ◽  
Resonant Problem

By means of Morse theory we prove the existence of a nontrivial solution to a superlinearp-harmonic elliptic problem with Navier boundary conditions having a linking structure around the origin. Moreover, in case of both resonance near zero and nonresonance at+∞the existence of two nontrivial solutions is shown.

WEAK SOLUTIONS OF QUASILINEAR BIHARMONIC PROBLEMS WITH POSITIVE, INCREASING AND CONVEX NONLINEARITIES

2008 ◽  
Vol 06 (03) ◽  
pp. 213-227 ◽  
Author(s):  
I. ABID ◽  
M. JLELI ◽  
N. TRABELSI
Keyword(s):  
Elliptic Equation ◽  
Boundary Conditions ◽  
Fourth Order ◽  
Weak Solutions ◽  
Source Term ◽  
Semilinear Elliptic Equation ◽  
Laplacian Operator ◽  
Navier Boundary Conditions ◽  
Semilinear Elliptic ◽  
Biharmonic Problems

We study the existence of positive weak solutions to a fourth-order semilinear elliptic equation with Navier boundary conditions and a positive, increasing and convex source term. We also prove the uniqueness of extremal solutions. In particular, we generalize results of Mironescu and Rădulescu for the bi-Laplacian operator.

scholarly journals Multiplicity of solutions for singular semilinear elliptic equations with critical Hardy-Sobolev exponents

2008 ◽  
Vol 2 (2) ◽  
pp. 158-174 ◽  
Author(s):  
Qianqiao Guo ◽  
Pengcheng Niu ◽  
Jingbo Dou
Keyword(s):  
Boundary Condition ◽  
Variational Methods ◽  
Elliptic Problem ◽  
Dirichlet Boundary Condition ◽  
Elliptic Equations ◽  
Dirichlet Boundary ◽  
Nontrivial Solutions ◽  
Existence And Multiplicity ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic

We consider the semilinear elliptic problem with critical Hardy-Sobolev exponents and Dirichlet boundary condition. By using variational methods we obtain the existence and multiplicity of nontrivial solutions and improve the former results.

Existence of non-trivial solutions for systems of n fourth order partial differential equations

2014 ◽  
Vol 64 (5) ◽  
Author(s):  
Shapour Heidarkhani
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Nontrivial Solution ◽  
Fourth Order ◽  
Local Minimum ◽  
Partial Differential ◽  
Navier Boundary Conditions ◽  
Minimum Theorem

AbstractIn this paper, employing a very recent local minimum theorem for differentiable functionals due to Bonanno, the existence of at least one nontrivial solution for a class of systems of n fourth order partial differential equations coupled with Navier boundary conditions is established.

Solution branches of a semilinear elliptic problem at corank-2 bifurcation points with Neumann boundary conditions

1993 ◽  
Vol 123 (3) ◽  
pp. 479-495 ◽  
Author(s):  
Mei Zhen
Keyword(s):  
Boundary Conditions ◽  
Elliptic Problem ◽  
Bifurcation Point ◽  
Continuation Method ◽  
Neumann Boundary ◽  
Neumann Boundary Conditions ◽  
Bifurcation Points ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic ◽  
Branch Switching

SynopsisSolution branches of a semilinear elliptic problem with Neumann boundary conditions are studied at its corank-2 bifurcation points. It is shown that generally there are exactly four different nontrivial solution branches passing through a corank-2 bifurcation point. The bifurcating solution branches are parametrised via a nonsingular enlarged problem. Branch switching at bifurcation points is incorporated with a continuation method.

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