بررسی وجود جواب‌های دسته‌ای از معادلات شرودینگر شبه خطی

نوع مقاله: مقاله پژوهشی

نویسندگان

گروه ریاضی، دانشگاه رازی

چکیده

در این مقاله به بررسی وجود یک جواب ضعیف نابدیهی برای دسته‌ای از معادلات شرودینگر شبه خطی در فضای سوبولف  می‌پردازیم. ابتدا از یک تغییر متغیر برای به دست آوردن یک تابعک انرژی خوش‌تعریف روی  استفاده می‌کنیم. سپس از یک منیفلد  به‌عنوان یک قید طبیعی استفاده کرده و ثابت می‌کنیم تحدید تابعک انرژی به این منیفلد اینفیمم خود را اختیار می‌کند. سرانجام ثابت می‌کنیم این نقطه‌ی اینفیمم یک جواب ضعیف نابدیهی برای معادله است.

کلیدواژه‌ها

موضوعات


عنوان مقاله [English]

On the existence of solutions to a class of semilinear Schrödinger equations

نویسندگان [English]

  • Yaghoob Jalilian
  • Iraj Dehsari
Department of Mathematics, Razi University, Kermanshah, Iran
چکیده [English]

In this paper, we investigate the existence of a nontrivial weak solution for a class of quasilinear Schrödinger equations in the Sobolev space . First, we use a change of variables to obtain a well defined energy functional on . Then we find a  manifold which is a natural constraint, and we prove that the restriction of the energy functional to this manifold attains its infimum. Finally, we show that this infimum point is a nontrivial weak solution for the equation.

کلیدواژه‌ها [English]

  • Quasilinear Schrödinger equation
  • Natural constraint
  • Nehari manifold
  • Weak solution
  • Existence of solution
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