Positive Solutions of Some Nonlinear Eigenvalue Problems

Existence of Positive Solutions for Nonlinear Eigenvalue Problems

Positive solutions and nonlinear multipoint conjugate eigenvalue problems ∗

Values of λ are determined for which there exist solutions in a cone of the n order nonlinear differential equation, u = λa(t)f(u), 0 < t < 1, satisfying the multipoint boundary conditions, u(ai) = 0, 0 ≤ j ≤ ni−1, 1 ≤ i ≤ k, where 0 = a1 < a2 < · · · < ak = 1, and ∑k i=1 ni = n, where a and f are nonnegative valued, and where both lim |x|→0+ f(x)/|x| and lim |x|→∞ f(x)/|x| exist.

Multiple Nontrivial Solutions for Nonlinear Eigenvalue Problems

In this paper we study a nonlinear eigenvalue problem driven by the p-Laplacian. Assuming for the right-hand side nonlinearity only unilateral and sign conditions near zero, we prove the existence of three nontrivial solutions, two of which have constant sign (one is strictly positive and the other is strictly negative), while the third one belongs to the order interval formed by the two opposi...

On the Existence and Multiplicity of Positive Solutions for Some Indefinite Nonlinear Eigenvalue Problem

This paper is concerned with the existence, uniqueness and/or multiplicity, and stability of positive solutions of an indefinite weight elliptic problem with concave or convex nonlinearity. We use mainly bifurcation methods to obtain our results.

Positive Solutions of Nonlinear Eigenvalue Problems for a Nonlocal Fractional Differential Equation

By using the fixed point theorem, positive solutions of nonlinear eigenvalue problems for a nonlocal fractional differential equation D 0 u t λa t f t, u t 0, 0 < t < 1, u 0 0, u 1 Σi 1αiu ξi are considered, where 1 < α ≤ 2 is a real number, λ is a positive parameter, D 0 is the standard Riemann-Liouville differentiation, and ξi ∈ 0, 1 , αi ∈ 0,∞ with Σi 1αiξ i < 1, a t ∈ C 0, 1 , 0,∞ , f t, u ...