| In this dissertation,we investigate existence and multiplicity results of solutions for some fractional quasilinear elliptic problems.In Chapter 1,we consider the following quasilinear equation where Ω(?)RN is bounded domain,1<q<p<r<ps*,λ is,positive constant,p*s=pN/(N-sp)is the critical Sobolev constant,(-△)ps is fractional p-Laplacian.By variational methods and analytical techniques,we attain existence and multiplicity results.In Chapter 2 we consider fractional p-q-Laplacian equation with perturbation where 0<s<1,sp<N,Ω is bounded domain in RN,λ is positive constant,f and g are continuous functions,ps*=pN/(N-sp)is the critical Sobolev constant,(-△)ps is fractional p-Laplacian,under different assumptions of nonlinearities,we give existence and multiplicity results respectively.Our approach is based on variational methods and some analytical techniques.In Chapter 3 we consider fractional quasilinear elliptic system where Ω is bounded domain in RN,0<s<1,1<q<p<p*s,and μ are positive constants,α+β＝p*s=pN/(N-sp)is critical Sobolev constant,(-△)ps is fractional p-Laplacian,under different assumptions on r,we attain multiplicity results respectively.In Chapter 4 we consider fractional quasilinear elliptic equation on RN where 0<s<1,1<r<p*s,λ is a positive constant,ps*=pN/(N-sp)is the fractional critical exponent and(-△)psis the fractional p-Laplacian operator.Under different assumptions on exponents,we obtain existence and multiplicity results respectively. |
