Study On Existence Results Of Fractional Quasilinear Elliptic Problems

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 ?(?)RN is bounded domain,1<q<p<r<ps*,? 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,? is bounded domain in RN,? 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 ? is bounded domain in RN,0<s<1,1<q<p<p*s,and ? are positive constants,?+??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,? 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.