Positive solutions for nonlinear m-point eigenvalue problems

Positive Solutions for Second-Order Three-Point Eigenvalue Problems

and Applied Analysis 3 Lemma 2.1. Suppose that G t, s is defined as above. Then we have the following results: 1 0 ≤ G t, s ≤ G s, s , 0 ≤ t, s ≤ 1, 2 G t, s ≥ ηtG s, s , 0 ≤ t, s ≤ 1. Proof. It is easy to see that 1 holds. To show that 2 holds, we distinguish four cases. i If t ≤ s ≤ η, then G t, s t ≥ ηts ηtG s, s . 2.4 ii If s ≤ t and s ≤ η, then G t, s s ≥ ηts ηtG s, s . 2.5 iii If t ≤ s an...

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 $n$th-order $m$-point boundary value problems

‎In this paper‎, ‎by using four functionals fixed point theorem‎, ‎we obtain sufficient conditions for the existence of‎ ‎at least one positive solution of an $n$th-order $m$-point boundary value problem‎. ‎As an application‎, ‎we give an example to demonstrate our main result.