Results 71 to 80 of about 129,456 (180)

Existence and multiplicity of positive solutions for a singular problem associated to the p-Laplacian operator

Electronic Journal of Differential Equations, 2004
Consider the problem $$ -Delta_{p}u=g(u) +lambda h(u)quadhbox{in }Omega $$ with $u=0$ on the boundary, where $lambdain(0,infty)$, $Omega$ is a strictly convex bounded and $C^{2}$ domain in $mathbb{R}^{N}$ with $Ngeq2$, and 1 less than $pleq2$.
Carlos Aranda, Tomas Godoy
doaj  

Positive periodic solutions and nonlinear eigenvalue problems for functional differential equations

Electronic Journal of Qualitative Theory of Differential Equations, 2012
This paper is devoted to investigate the existence of positive periodic solution for a functional differential equation in the form of $\lambda\mathbb{L}x=-b(t)f(x(t-\tau(t))),$ where $\mathbb{L}x=x'(t)-a(t)g(x(t))x(t)$.
Xuemei Zhang
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On the average value for nonconstant eigenfunctions of the p-Laplacian assuming Neumann boundary data

Electronic Journal of Differential Equations, 2003
We show that nonconstant eigenfunctions of the $p$-Laplacian do not necessarily have an average value of 0, as they must when $p=2$. This fact has implications for deriving a sharp variational characterization of the second eigenvalue for a general class
Stephen B. Robinson
doaj  

Existence of nodal solutions to some nonlinear boundary value problems for ordinary differential equations of fourth order

Electronic Journal of Qualitative Theory of Differential Equations
In this paper, we study the existence of nodal solutions of some nonlinear boundary value problems for ordinary differential equations of fourth order with a spectral parameter in the boundary condition.
Ziyatkhan Aliyev, Yagut Aliyeva
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Existence of positive solutions for two nonlinear eigenvalue problems

Electronic Journal of Differential Equations, 2003
We study the existence of positive solutions for the following two nonlinear eigenvalue problems $$displaylines{ Delta u-g(.,u)u+lambda f(.,u)u=0, cr Delta u-g(.,u)u+lambda f(.,u)=0, }$$ in a bounded regular domain in $mathbb{R}^{2}$ with $u=0$ on the ...
Nedra Belhaj Rhouma, Lamia Maatoug
doaj  

Basic results on nonlinear eigenvalue problems of fractional order

Electronic Journal of Differential Equations, 2012
In this article, we discuss the basic theory of boundary-value problems of fractional order $1 < delta < 2$ involving the Caputo derivative. By applying the maximum principle, we obtain necessary conditions for the existence of eigenfunctions ...
Mohammed Al-Refai
doaj  

Parameters and solutions of linear and nonlinear oscillators

International Journal of Mathematics and Mathematical Sciences, 1979
Relationship between existence of solutions for certain classes of nonlinear boundary value problems and the smallest or the largest eigenvalue of the corresponding linear problem is obtained.
Rina Ling
doaj   +1 more source

On local compactness in quasilinear elliptic problems

, 2007
One of the major difficulties in nonlinear elliptic problems involving critical nonlinearities is the compactness of Palais-Smale sequences. In their celebrated work \cite{BN}, Br\'ezis and Nirenberg introduced the notion of critical level for these ...
Adriouch, Khalid, Hamidi, Abdallah El
core   +2 more sources

Comparison between the Variational Iteration Method and the Homotopy Perturbation Method for the Sturm-Liouville Differential Equation

Boundary Value Problems, 2010
We applied the variational iteration method and the homotopy perturbation method to solve Sturm-Liouville eigenvalue and boundary value problems. The main advantage of these methods is the flexibility to give approximate and exact solutions to both ...
R. Darzi, A. Neamaty
doaj   +1 more source

Note on a Nonlinear Eigenvalue Problem

Rocky Mountain Journal of Mathematics, 1993
Consider the nonlinear eigenvalue problem \({d \over dx} (| u' |^{p-2}u')+ \lambda | u |^{p-2}u=0\). It is observed that the first positive eigenvalue \(\lambda_ p\) satisfies a conjugacy condition \(\lambda_ p^{1/p}=\lambda_ q^{1/p}\), \({1 \over p} + {1 \over q}=1\). Also the corresponding eigenfunctions are related.
openaire   +2 more sources