scholarly journals Symmetric mountain pass lemma and sublinear elliptic equations

2016 ◽  
Vol 260 (3) ◽  
pp. 2587-2610 ◽  
Author(s):  
Ryuji Kajikiya
Keyword(s):  
Elliptic Equations ◽  
Mountain Pass ◽  
Mountain Pass Lemma ◽  
Symmetric Mountain Pass Lemma

scholarly journals The Existence of a Nontrivial Solution for a -Kirchhoff Type Elliptic Equation in

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Zonghu Xiu
Keyword(s):  
Elliptic Equation ◽  
Nontrivial Solution ◽  
Elliptic Equations ◽  
Mountain Pass ◽  
Mountain Pass Lemma ◽  
Kirchhoff Type

Using Mountain Pass lemma, under some appropriate assumptions, we establish the existence of one nontrivial solution for a class ofp-Kirchhoff-type elliptic equations in .

scholarly journals Multiple Solutions for Generalized Asymptotical Linear Hamiltonian Systems Satisfying Bolza Boundary Conditions

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Yuan Shan ◽  
Baoqing Liu
Keyword(s):  
Boundary Conditions ◽  
Hamiltonian Systems ◽  
Multiple Solutions ◽  
Index Theory ◽  
Mountain Pass ◽  
Mountain Pass Lemma ◽  
Multiplicity Of Solutions ◽  
Existence And Multiplicity ◽  
Linear Hamiltonian Systems ◽  
Symmetric Mountain Pass Lemma

This paper is devoted to multiple solutions of generalized asymptotical linear Hamiltonian systems satisfying Bolza boundary conditions. We classify the linear Hamiltonian systems by the index theory and obtain the existence and multiplicity of solutions for the Hamiltonian systems, based on an application of the classical symmetric mountain pass lemma.

scholarly journals Infinitely Many Solutions for a Class of Fractional Impulsive Coupled Systems with (p,q)-Laplacian

2018 ◽  
Vol 2018 ◽  
pp. 1-14 ◽  
Author(s):  
Junping Xie ◽  
Xingyong Zhang
Keyword(s):  
Mixed Type ◽  
Coupled Systems ◽  
Mountain Pass ◽  
Mountain Pass Lemma ◽  
Infinitely Many Solutions ◽  
Symmetric Mountain Pass Lemma

By using the symmetric mountain pass lemma, we investigate the problem of existence of infinitely many solutions for a class of fractional impulsive coupled systems with (p,q)-Laplacian, which possesses mixed type nonlinearities, and the nonlinearities do not need to satisfy the well-known Ambrosetti-Rabinowitz condition.

scholarly journals Periodic Solutions of a Class of Fourth-Order Superlinear Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Yanyan Li ◽  
Yuhua Long
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Fourth Order ◽  
Nonlinear Term ◽  
Single Equation ◽  
Mountain Pass ◽  
Mountain Pass Lemma ◽  
Variational Techniques ◽  
Superlinear Growth ◽  
Symmetric Mountain Pass Lemma

This paper deals with the periodic solutions of a class of fourth-order superlinear differential equations. By using the classical variational techniques and symmetric mountain pass lemma, the periodic solutions of a single equation in literature are extended to that of equations, and also, the cubic growth of nonlinear term is extended to a general form of superlinear growth.

Fractional elliptic equations with critical exponential nonlinearity

2016 ◽  
Vol 5 (1) ◽  
pp. 57-74 ◽  
Author(s):  
Jacques Giacomoni ◽  
Pawan Kumar Mishra ◽  
K. Sreenadh
Keyword(s):  
Positive Solutions ◽  
Elliptic Equations ◽  
Multiple Solutions ◽  
Fractional Laplacian ◽  
Nehari Manifold ◽  
Mountain Pass ◽  
Laplacian Operator ◽  
Exponential Nonlinearity ◽  
Existence Of Positive Solutions ◽  
Fractional Laplacian Operator

AbstractWe study the existence of positive solutions for fractional elliptic equations of the type (-Δ)1/2u = h(u), u > 0 in (-1,1), u = 0 in ℝ∖(-1,1) where h is a real valued function that behaves like eu2 as u → ∞ . Here (-Δ)1/2 is the fractional Laplacian operator. We show the existence of mountain-pass solution when the nonlinearity is superlinear near t = 0. In case h is concave near t = 0, we show the existence of multiple solutions for suitable range of λ by analyzing the fibering maps and the corresponding Nehari manifold.

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.

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
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