The Study Of Nonlinear Partial Differential Equations

In this paper,making use of Some conventional thcory tools Such as mountain pass lemmaa,(PS)condition.Critical point theory,the paper are concerned with the existence re-sult of positive solutions for a quasilinear elliptic equation arising from plasma physics.By means of make a change of variable convert a quasilinear elliptic equation into a semilin-ear one and show the existence result for original equation under the Suitable conditions on the power of nonlinearity and quasilincarity.At chapter II,using variational methods combined with Jeanjean’s result[24],we study the existence of nontrivial solutions for quasilinear Schrodinger equation where V:RNâ†'R is a continuous function，N≥3. In this chatper note that the solutions of(1一10)are the critical points of the following functional where H(u)=∫0uh(s)ds.Because of the functional t(u)may not be well defined in the usual Sobolev space H1(RN).Hence make a change of variables as v=G(u)=∫0ug(t)dt, where g(t)=(?)1+a2t22(1+t2)2-x.Since g(t) is monotonous with|t|,the inverse function G-1(t)of G(t)exists.Then after the change of variables,I(u) can be writton by Thus J is well defined in H1(RN)and J C C1. Finally,we find in order to find the nontrivial solutions of(1-10),it Suffices to study the existence of the nontrivial solutions of the following equations...