On the Existence of Nontrivial Solutions of Quasi-asymptotically Linear Problem for the P-Laplacian

2002 ◽  
Vol 18 (4) ◽  
pp. 599-606
Author(s):  
Zhi-hui Chen ◽  
Yao-tian Shen
Keyword(s):  
Linear Problem ◽  
Nontrivial Solutions ◽  
Asymptotically Linear ◽  
Asymptotically Linear Problem

Multiple solutions for an asymptotically linear problem in

2004 ◽  
Vol 56 (1) ◽  
pp. 1-18
Author(s):  
A.M. Micheletti ◽  
C. Saccon
Keyword(s):  
Multiple Solutions ◽  
Linear Problem ◽  
Asymptotically Linear ◽  
Asymptotically Linear Problem

Bifurcation from infinity for an asymptotically linear problem on the half-line

2011 ◽  
Vol 74 (13) ◽  
pp. 4533-4543 ◽  
Author(s):  
François Genoud
Keyword(s):  
Linear Problem ◽  
Half Line ◽  
Asymptotically Linear ◽  
Bifurcation From Infinity ◽  
Asymptotically Linear Problem

scholarly journals Periodic solutions for a fractional asymptotically linear problem

2018 ◽  
Vol 149 (03) ◽  
pp. 593-615
Author(s):  
Vincenzo Ambrosio ◽  
Giovanni Molica Bisci
Keyword(s):  
Neumann Boundary ◽  
Index Theory ◽  
Careful Analysis ◽  
Asymptotically Linear ◽  
Existence And Multiplicity ◽  
Degenerate Elliptic ◽  
Subcritical Nonlinearity ◽  
Fractional Spaces ◽  
Non Local ◽  
Asymptotically Linear Problem

We study the existence and multiplicity of periodic weak solutions for a non-local equation involving an odd subcritical nonlinearity which is asymptotically linear at infinity. We investigate such problem by applying the pseudo-index theory developed by Bartolo, Benci and Fortunato [11] after transforming the problem to a degenerate elliptic problem in a half-cylinder with a Neumann boundary condition, via a Caffarelli-Silvestre type extension in periodic setting. The periodic nonlocal case, considered here, presents, respect to the cases studied in the literature, some new additional difficulties and a careful analysis of the fractional spaces involved is necessary.

scholarly journals Comment on “Unilateral Global Bifurcation from Intervals for Fourth-Order Problems and Its Applications”

2017 ◽  
Vol 2017 ◽  
pp. 1-3
Author(s):  
Ziyatkhan Aliyev
Keyword(s):  
Recent Work ◽  
Comparison Theorem ◽  
Fourth Order ◽  
Linear Problem ◽  
Eigenvalue Problems ◽  
Global Bifurcation ◽  
Nontrivial Solutions ◽  
Nodal Solutions ◽  
Negative Eigenvalues ◽  
Fourth Order Problems

In the recent paper W. Shen and T. He and G. Dai and X. Han established unilateral global bifurcation result for a class of nonlinear fourth-order eigenvalue problems. They show the existence of two families of unbounded continua of nontrivial solutions of these problems bifurcating from the points and intervals of the line trivial solutions, corresponding to the positive or negative eigenvalues of the linear problem. As applications of this result, these authors study the existence of nodal solutions for a class of nonlinear fourth-order eigenvalue problems with sign-changing weight. Moreover, they also establish the Sturm type comparison theorem for fourth-order problems with sign-changing weight. In the present comment, we show that these papers of above authors contain serious errors and, therefore, unfortunately, the results of these works are not true. Note also that the authors used the results of the recent work by G. Dai which also contain gaps.

Existence of three nontrivial solutions for asymptotically -linear noncoercive -Laplacian equations

2011 ◽  
Vol 74 (16) ◽  
pp. 5314-5326 ◽  
Author(s):  
Nikolaos S. Papageorgiou ◽  
Eugénio M. Rocha
Keyword(s):  
Nontrivial Solutions ◽  
Asymptotically Linear ◽  
Laplacian Equations

scholarly journals DIRICHLET BVP FOR THE SECOND ORDER NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS AT RESONANCE

2019 ◽  
Vol 24 (4) ◽  
pp. 585-597
Author(s):  
Sulkhan Mukhigulashvili ◽  
Mariam Manjikashvili
Keyword(s):  
Dirichlet Problem ◽  
Differential Equations ◽  
Nonlinear Equation ◽  
Linear Equation ◽  
Linear Problem ◽  
Sufficient Conditions ◽  
Nonlinear Ordinary Differential Equations ◽  
Nontrivial Solutions ◽  
At Resonance ◽  
Carathéodory Function

Landesman-Lazer’s type efficient sufficient conditions are established forthe solvability of the Dirichlet problem u′′(t) = p(t)u(t) + f(t, u(t)) + h(t),for a ≤ t ≤ b, u(a) = 0, u(b) = 0, where h, p ϵ L([a, b];R) and f is the L([a, b];R) Caratheodory function, in the casewhere the linear problem u′′(t) = p(t)u(t), u(a) = 0,u(b) = 0 has nontrivial solutions. The results obtained in the paper are optimal in the sense that if f ≡ 0,i.e., when nonlinear equation turns to the linear equation, from our results follows the first partof Fredholm’s theorem.

Sign in / Sign up

Export Citation Format

Share Document