Existence of solutions for a class of first order boundary value problems

Abstract

In this work, we are interested in the existence of solutions for a class of first order boundary value problems (BVPs for short). We give new sufficient conditions under which the considered problems have at least one solution, one nonnegative solution and two non trivial nonnegative solutions, respectively. To prove our main results we propose a new approach based upon recent theoretical results. The results complement some recent ones.

Existence of Solutions for Two-Point Integral Boundary Value Problems with Impulses

“…Theorem 2.6. [17,Theorem 2.8] Let U 1 ,U 2 and U 3 three open bounded subsets of P such that U 1 ⇢ U 2 ⇢ U 3 and 0 2 U 1 . Assume that T :Ω!…”

Classical solutions for the generalized Kadomtsev–Petviashvili I equations

“…Moreover, we will formulate the basic fixed-point theorems which we explore to prove our main results. For more details, we refer the reader to the papers [10][11][12][13][14] and references therein. To prove the existence of at least one global classical solution for the IVP (1.1), we will use the following fixed-point theorem.…”

“…The next result is a fixed-point theorem which we will use to prove the existence of at least two nonnegative global classical solutions of the IVP (1.1). For its proof, we refer the reader to the paper [14].…”