Existence and global exponential stability of almost periodic solutions for SICNNs with nonlinear behaved functions and mixed delays.
In the paper, we obtain the existence of symmetric or monotone positive solutions and establish a corresponding iterative scheme for the equation , , where , , subject to nonlinear boundary condition. The main tool is the monotone iterative technique. Here, the coefficient may be singular at .
We prove the existence of a positive solution to the BVP imposing some conditions on Φ and f. In particular, we assume to be decreasing in t. Our method combines variational and topological arguments and can be applied to some elliptic problems in annular domains. An bound for the solution is provided by the norm of any test function with negative energy.
Some sufficient conditions on the existence and multiplicity of solutions for the damped vibration problems with impulsive effects ⎧ u”(t) + g(t)u’(t) + f(t,u(t)) = 0, a.e. t ∈ [0,T ⎨ u(0) = u(T) = 0 ⎩ , j = 1,...,p, are established, where , g ∈ L¹(0,T;ℝ), f: [0,T] × ℝ → ℝ is continuous, and , j = 1,...,p, are continuous. The solutions are sought by means of the Lax-Milgram theorem and some critical point theorems. Finally, two examples are presented to illustrate the effectiveness of our results....
We use the genus theory to prove the existence and multiplicity of solutions for the fractional -Kirchhoff problem where is an open bounded smooth domain of , , with fixed, , is a numerical parameter, and are continuous functions.
This paper discusses the existence and multiplicity of solutions for a class of -Kirchhoff type problems with Dirichlet boundary data of the following form where is a smooth open subset of and with , , are positive constants and is a continuous function. The proof is based on critical point theory and variable exponent Sobolev space theory.