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In this paper we deal with the boundary value problem in the Hilbert space. Existence of a solutions is proved by using the method of lower and upper solutions. It is not necessary to suppose that the homogeneous problem has only the trivial solution. We use some results from functional analysis, especially the fixed-point theorem in the Banach space with a cone (Theorem 4.1, [5]).

Existence of solutions for a certain differential inclusion of third order.

Cernea, A. (2009)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Existence of solutions for a class of boundary value problems for the equation $x^{''} = F (t, x, x^{'}, x^{''})$

Antonio R. Tineo (1988)

Commentationes Mathematicae Universitatis Carolinae

Existence of solutions for a class of damped vibration problems on time scales.

Li, Yongkun, Zhou, Jianwen (2010)

Advances in Difference Equations [electronic only]

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

Amirouche Mouhous a, Svetlin Georgiev Georgiev b, Karima Mebarki c (2022)

Archivum Mathematicum

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 a class of fourth-order $m$ -point boundary value problems.

Sun, Jian-Ping, Ren, Qiu-Yan (2010)

Electronic Journal of Qualitative Theory of Differential Equations [electronic only]

Existence of solutions for a class of second-order $p$ -Laplacian systems with impulsive effects

Peng Chen, Xianhua Tang (2014)

Applications of Mathematics

The purpose of this paper is to study the existence and multiplicity of a periodic solution for the non-autonomous second-order system $\begin{matrix} \frac{d}{d t} (| \dot{u} (t) |^{p - 2} \dot{u} (t)) = \nabla F (t, u (t)), a.e. t \in [0, T], \\ u (0) - u (T) = \dot{u} (0) - \dot{u} (T) = 0, \\ Δ {\dot{u}}^{i} (t_{j}) = {\dot{u}}^{i} (t_{j}^{+}) - {\dot{u}}^{i} (t_{j}^{-}) = I_{i j} (u^{i} (t_{j})), i = 1, 2, \dots, N; j = 1, 2, \dots, m . \end{matrix}$ By using the least action principle and the saddle point theorem, some new existence theorems are obtained for second-order $p$ -Laplacian systems with or without impulse under weak sublinear growth conditions, improving some existing results in the literature.

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