On Semilinear Problems with Nonlinearities Depending Only on Derivatives

Existence of Solutions to u″+u+g(t,u,u′)=p(t),u(0)=u(π)=0

“…Also in the case of (g1), as shown in [2], using a result of ([1], Theorem 3.1), problem (1.3) has a solution. Hence, we can state the following result, which essentially is due to Canada and Drabek [2]. Remark 3.1.…”

“…where g and p are continuous functions, has been studied (e.g., by Canada and Drabek [2] and Habets and Sanchez [3]). The existence results of [2] are completed in [3] by a multiplicity result in terms of conditions forp in the decomposition of p, p t =p sin t +p t (1.2)…”

“…The existence results of [2] are completed in [3] by a multiplicity result in terms of conditions forp in the decomposition of p, p t =p sin t +p t (1.2)…”

“…The proofs are based on the alternative method (as in [2] and [3]), a connectedness result of [6], the contraction mapping principle, and a detailed analysis of the bifurcation equation utilizing, e.g., a generalization of the mean value theorem for integrals [5]. We shall obtain results for (1.3) with g bounded or unbounded, having finite limits at ±∞ or without limits.…”

An Existence Result for Neumann Type Boundary Value Problems for Second Order Nonlinear Functional Differential Equation

“…We note that the solvability of problem (5) is not addressed in paper [12] when h in (5) is unbounded, and there is no paper concerned with the solvability of Neumann boundary value problems for second order functional differential equations.…”