Positive Solutions for 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 and eigenvalue intervals for nonlinear systems

Positive solutions and eigenvalue intervals for nonlinear systems JIFENG CHU1,2, DONAL O’REGAN3 and MEIRONG ZHANG1 1Department of Mathematical Sciences, Tsinghua University, Beijing 100 084, China 2Department of Applied Mathematics, Hohai University, Nanjing 210 098, China 3Department of Mathematics, National University of Ireland, Galway, Ireland E-mail: [email protected]; [email protected]...

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 ...