بررسی وجود جواب نوعی ازمعادله مرتبه چهاربای لاپلاسین و مشاهده ناپیوستگی طیف جوابها

نویسنده
دانشگاه علم وصنعت ایران
چکیده
دراین مقاله به بررسی وجود جواب معادله ∆^2 u+c∆u+ε div(φ(x,∇u)∇u)=λu+εf(x,u) با شرایط مرزی ناویرu=Δu=0 روی مرزهموار ناحیه کراندار Ω از R^N می پردازیم که در آن ε و λ پارامترهایی مثبت و c<μ_1 که μ_1 کوچکترین مقدار ویژه عملگر لاپلاس با شرایط مرزی دیریکله است. با ارائه بحثهایی مبتنی بر حساب تغییرات و تکیه بر قضیه نقطه ثابت باناخ، وجود جواب معادله به ازای هر 0<λ در شرایطی که ε≠0 به عنوان یک پدیده ناپیوسته در مقابل حالتی که ε=0 و معادله لزوما دارای جواب ضعیف نیست، مطرح می شود.
کلیدواژه‌ها

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