Existence of nontrivial solutions for double phase problems with logarithmic non-linearity
This paper studies the nontrivial solution of a class of double phase problem with logarithmic nonlinear-ity.The nonlinearity of the double phase problem is usually polynomial,but the nonlinearity in this paper is logarith-mic nonlinearity.Through calculation,we can see that the energy functional of this kind of double phase problem with logarithmic nonlinearity satisfies the mountain geometry structure.The Palais-Smale condition is obtained through bounded sequence and the existence of the nontrivial solutions of the problem is obtained by mountain pass lemma.
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