Positive Solutions Of Quasilinear Equations With Hardy Potential

In this thesis, we will be concerned with the existence of solutions for the following eqautions whereΩis a domain of RN with the smooth boundary (?)Q,Δpu= div(|▽u|p-2▽u) is the p-Laplacian, 1< p< N,λ>0 is a parameter,0≤μ< ((N-p)/p)p(?)μ, the nonlinear term h:Ω×R→[0,∞) is a nonnegative function, h has a p-asymptotically linear growth near zero and has a p-superlinear growth at infinity, and h satifies some other conditions.In this thesis, by using the variational techniques, sub and super solution method, the mountain pass lemma and the comparison principle, we obtian that the equation(Pλ) has at least one positive solution under both cases of 0<λ<λ1,b andλ=λ1,b, and the equation (Pa) has at least two positive solutions in the case ofλ>λ1,b, whereλ1,b is the first eigenvalue of the following eigenvalue problem for some weight function b(x)€L∞(Ω). Moreover we discuss the asymptotic behavior of the solution whenλ→0 andλ→λ1,b+.