With the increasing carrier frequency in next-generation wireless networks, conventional discrete aperture arrays (DAPA) are unable to fully meet the growing demands of sixth-generation wireless networks. To provide a higher degree of freedom, the continuous-aperture array (CAPA) technique emerges as a promising solution for next-generation networks. In this article, a CAPA-aided network is proposed to deliver access services to multiple users. The transmission power of a two-user pair in the downlink is optimized by using the Fourier transformation to derive tractable results. With the aid of Karush-Kuhn-Tucker (KKT) conditions, closed-form expressions for both orthogonal multiple access (OMA) and non-orthogonal multiple access (NOMA) are derived. Time division multiple access (TDMA) and spatial division multiple access (SDMA) are also considered as OMA schemes. Furthermore, DAPA is included as a benchmark for comparison. Our analytical and numerical results demonstrate the following: i) The proposed KKT-based approach achieves optimal performance in transmission power; ii) The minimal required transmission power for NOMA is lower than that for the OMA benchmark schemes; iii) A performance gap is observed between CAPA and DAPA in both NOMA and OMA, emphasizing the advantages of CAPA-aided networks.