A semilinear elliptic problem involving nonlinear boundary condition and sign-changing potential

• الحاوية / القاعدة: Electronic Journal of Differential Equations
• المؤلف الرئيسي: Tsung-Fang Wu
• التنسيق: مقال
• اللغة: الإنجليزية
• منشور في: Texas State University 2006-10-01
• الموضوعات: Semilinear elliptic equations; Nehari manifold; Nonlinear boundary condition.
• الوصول للمادة أونلاين: http://ejde.math.txstate.edu/Volumes/2006/131/abstr.thml
• تدمد: 1072-6691

In this paper, we study the multiplicity of nontrivial nonnegative solutions for a semilinear elliptic equation involving nonlinear boundary condition and sign-changing potential. With the help of the Nehari manifold, we prove that the semilinear elliptic equation: $$displaylines{ -Delta u+u=lambda f(x)|u|^{q-2}u quad hbox{in }Omega , cr frac{partial u}{partial u }=g(x)|u| ^{p-2}u quad hbox{on }partial Omega , }$$has at least two nontrivial nonnegative solutions for $lambda $is sufficiently small.