| The work of this thesis deals with existence and nonexistence of solutions for semilinear elliptic and parabolic equations on bounded domains in RN. This is an interesting and a widely investigated field.(â… ) The general form of the elliptic equations under Dirichlet boundary con-dition that we study is whereΩis a bounded domain with smooth boundary in RN(N≥3), x = (y, z)∈Ω(?) Rk×RN-k = RN-, 2≤k1 are fixed parameters.The various functions are essentially pure power functions. The function f0(u) behaves lik, |u|γand the other functions fi(u) all behave like |u|β.The result without the fi is well-known and first proved in [41]. Our treat-ment differs from [17], in that we use a different space.Here, the proof of existence result is based on a contraction mapping argu-ment in an appropriate space of functions which yields global in time solutions automatically. |
