This paper studies the existence of positive solutions of the Dirichlet problem for the nonlinear equation involving p-Laplacian operator: -△pu = λf(u) on a bounded smooth domain Ω in Rn. The authors extend part of...This paper studies the existence of positive solutions of the Dirichlet problem for the nonlinear equation involving p-Laplacian operator: -△pu = λf(u) on a bounded smooth domain Ω in Rn. The authors extend part of the Crandall-Rabinowitz bifurcation theory to this problem. Typical examples are checked in detail and multiplicity of the solutions are illustrated. Then the stability for the associated parabolic equation is considered and a Fujita-type result is presented.展开更多
In this note, we establish some estimates of solutions of the scalar Ginzburg-Landau equation and other nonlinear Laplacian equation △u =f(x, u). This will give an estimate of the Hausdorff dimension for the free bou...In this note, we establish some estimates of solutions of the scalar Ginzburg-Landau equation and other nonlinear Laplacian equation △u =f(x, u). This will give an estimate of the Hausdorff dimension for the free boundary of the obstacle problem.展开更多
基金Project supported by the 973 Project of the Ministry of Science and Technology of China (No.G1999075107) a Scientific Grant of Tsinghua University.
文摘This paper studies the existence of positive solutions of the Dirichlet problem for the nonlinear equation involving p-Laplacian operator: -△pu = λf(u) on a bounded smooth domain Ω in Rn. The authors extend part of the Crandall-Rabinowitz bifurcation theory to this problem. Typical examples are checked in detail and multiplicity of the solutions are illustrated. Then the stability for the associated parabolic equation is considered and a Fujita-type result is presented.
文摘In this note, we establish some estimates of solutions of the scalar Ginzburg-Landau equation and other nonlinear Laplacian equation △u =f(x, u). This will give an estimate of the Hausdorff dimension for the free boundary of the obstacle problem.
