Positive Solutions of a Nonlinear Elliptic Equation Involving a Singular Term

  • Arij Bouzelmate LaR2A Laboratory, Faculty of Sciences, Abdelmalek Essaadi University, Tetouan, 93000, Morocco
  • Hikmat El Baghouri LaR2A Laboratory, Faculty of Sciences, Abdelmalek Essaadi University, Tetouan, 93000, Morocco
  • Fatima Sennouni LaR2A Laboratory, Faculty of Sciences, Abdelmalek Essaadi University, Tetouan, 93000, Morocco

Анотація

У цій роботі ми досліджуємо існування та єдиність додатних розв'язків рівняння $\Delta_p\, u=f(\vert x \vert)/u(x)$, $x\in \mathbb{R}^{N}$, де $N > p > 2$. Точніше, за певних припущень щодо функції $f$ ми даємо відповідь на питання про глобальне існування, сформульоване в роботі [14], використовуючи теорію інваріантних многовидів у динамічних системах та енергетичний метод. Крім того, ми проводимо детальний аналіз асимптотичної поведінки розв'язків за допомогою логарифмічних перетворень.

Mathematical Subject Classification 2020: 35A01, 35A02, 35B08, 35B09, 35B40, 35J60, 35J65

Ключові слова:

існування, єдиність, додатний розв'язок, асимптотична поведінка, тотожність Похожаєва, динамічна система

Посилання

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A. Bouzelmate, H. E. Baghouri, F. Sennouni, Positive Solutions of a Nonlinear Elliptic Equation Involving a Singular Term, Журн. мат. фіз. анал. геом. 21 (2025), 160–178.

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Том 21 № 2 (2025)

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