Positive solutions of convex 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...

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 ...

Existence of Positive Solutions for Singular Eigenvalue Problems

In this paper, we discuss the existence, nonexistence, and multiplicity of positive solutions for a class of singular eigenvalue problems. Some of our theorems are new, while others extend earlier results obtained by Zhang and Kong [12]. The interesting point is that the authors obtain the relation between the existence of solutions and the parameter λ. The arguments are based on the fixed poin...