Large language models (LLMs) are increasingly used in clinical and care settings. This exploratory study investigates whether LLMs exhibit sycophantic behavior - adapting their responses to social expectation signals rather than maintaining professional quality - in the context of dementia care. Five prompts with systematically increasing confirmatory and authority-related framing (P1 neutral to P5 authority-signaled implementation support) were submitted to four LLMs (GPT-5, Claude Sonnet 4.6, Gemini 3.1 Pro, Mistral Large), each repeated five times (N = 100 responses). Responses were evaluated using an LLM-as-a-Judge methodology against seven nursing-ethical quality criteria (K1-K7) and a tone scale (0-3). All models showed significant negative Spearman correlations between prompt level and response quality (rho ranging from -0.543 to -0.734, all p < 0.01). Mistral Large exhibited the most pronounced effect (rho = -0.734), with mean scores dropping from 6.0/7 at P1 to 0.2/7 at P5. The findings suggest that LLMs pose context-sensitive risks in high-stakes care environments and that prompt framing significantly shapes response quality - a dimension that has received insufficient attention in healthcare AI deployment.