LargeH-surfaces via the mountain-pass-lemma

1985 ◽  
Vol 270 (3) ◽  
pp. 441-459 ◽  
Author(s):  
Michael Struwe
Keyword(s):  
Mountain Pass ◽  
Mountain Pass Lemma

scholarly journals On the Existence of Nontrivial Solutions for Nonlocal Elliptic Kirchhoff Type Problems with Nonlinear Boundary Conditions

2015 ◽  
Vol 55 (1) ◽  
pp. 183-188
Author(s):  
S. H. Rasouli ◽  
B. Salehi
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Type Equation ◽  
Nonlinear Boundary Conditions ◽  
Mountain Pass ◽  
Mountain Pass Lemma ◽  
Nontrivial Solutions ◽  
Kirchhoff Type ◽  
Kirchhoff Type Equation ◽  
Kirchhoff Type Problems

Abstract In this paper, by using the Mountain Pass Lemma, we study the existence of nontrivial solutions for a nonlocal elliptic Kirchhoff type equation together with nonlinear boundary conditions.

scholarly journals Homoclinic solutions of 2nth-order difference equations containing both advance and retardation

2016 ◽  
Vol 14 (1) ◽  
pp. 520-530 ◽  
Author(s):  
Yuhua Long ◽  
Yuanbiao Zhang ◽  
Haiping Shi
Keyword(s):  
Difference Equation ◽  
Critical Point ◽  
Difference Equations ◽  
Homoclinic Solutions ◽  
Mountain Pass ◽  
Nonlinear Difference Equation ◽  
Mountain Pass Lemma ◽  
Order Difference ◽  
Existence And Multiplicity ◽  
New Criteria

AbstractBy using the critical point method, some new criteria are obtained for the existence and multiplicity of homoclinic solutions to a 2nth-order nonlinear difference equation. The proof is based on the Mountain Pass Lemma in combination with periodic approximations. Our results extend and improve some known ones.

scholarly journals Boundary Value Problems for Fourth Order Nonlinearp-Laplacian Difference Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Qinqin Zhang
Keyword(s):  
Difference Equation ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Difference Equations ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Mountain Pass ◽  
Mountain Pass Lemma

We consider the boundary value problem for a fourth order nonlinearp-Laplacian difference equation containing both advance and retardation. By using Mountain pass lemma and some established inequalities, sufficient conditions of the existence of solutions of the boundary value problem are obtained. And an illustrative example is given in the last part of the paper.

PROFILE OF SOLUTIONS WITH SHARP LAYERS TO SOME SINGULARLY PERTURBED QUASILINEAR DIRICHLET PROBLEMS

2003 ◽  
Vol 05 (06) ◽  
pp. 883-920 ◽  
Author(s):  
ZONGMING GUO ◽  
J. R. L. WEBB
Keyword(s):  
Positive Solution ◽  
Bounded Domain ◽  
Mountain Pass ◽  
Singularly Perturbed ◽  
Singularly Perturbed Problem ◽  
Mountain Pass Lemma ◽  
Dirichlet Problems ◽  
Large Solution ◽  
Small Solution

The singularly perturbed problem for the p-Laplacian [Formula: see text] is studied in a convex bounded domain Ω containing 0 when p > 2, f(0) = 0 and f has precisely 3 positive zeros. There exist a small solution [Formula: see text] and a large solution [Formula: see text] when ε is sufficiently small. By using the mountain pass lemma we show there is an intermediate positive solution uε and we study the structure of this solution.

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